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The problem solver鈥檚 path in graph theory

A portrait of J酶rgen Bang-Jensen, who, from the beginning of this spring, has entered the position of Professor Emeritus at the Department of Mathematics and Computer Science, 糖果派对.

By Ursula Lundgreen, , 3/28/2025

Jørgen Bang-Jensen sits back calmly on the sofa, looking at me with a prepared expression. Before the interview, he had, like an intelligence agent, sent me two pages describing who he is—just in case I was in doubt. It is crystal clear that he is a man who prefers to be prepared.

– I like to have things under control in advance. Some people find that a bit silly, but there have been situations where it has been crucial that I had everything in order from the start, he says.

He has put IMADA on the world map and is today one of Denmark鈥檚 most internationally recognized mathematicians.

Bjarne Toft, Associate Professor Emeritus

And that applies not only in academic settings. He is indeed the type who has already found the solution before others even notice there’s a problem. -I think my approach has often benefited others.

– I’ve often solved the problem before it even reaches anyone else’s ears, he says with a wry smile.

And there’s a reason why Jørgen has adopted this ‘belt-and-suspenders’ approach to life and tasks in general—because as a teenager, he often had to think on his feet, ready to receive unexpected patients in his father’s medical clinic. The more you can prepare for even spontaneous situations, the better.

Meet the researcher

J酶rgen Bang-Jensen is now Professor Emeritus at the Department of Mathematics and Computer Science at the University of Southern Denmark in Odense.

Contact

J酶rgen Bang Jensen as a young student

From a medical family to a mathematical passion 

Jørgen grew up on the dansish island Langeland in a family where knowledge and analytical thinking were a natural part of everyday life. In 1964, his father swapped a position as a neurosurgeon at Copenhagen University Hospital – Rigshospitalet,  for life as a general practitioner with his own clinic on the southern part of Langeland. At the dinner table, he often talked about everything from complex surgeries to unruly diseases.

– He would have an opinion on almost anything,  says Jørgen, and his father’s ability to remember details and see connections became a great inspiration for Jørgen and his siblings.

– I’ll never forget the time a man stood at our doorstep, with his thumb dangling by a thin strip of skin, asking if my father was home so that he could cut it off! That experience, along with countless others in the same category, taught me to go from 0 to 100 in record time, Jørgen explains, his eyes widening slightly at the somewhat gory childhood memory.

Fortunately, it wasn’t just bloody memories that taught him decisiveness. His strong relationship with his mother was also central.

– My mother was a very creative person who taught us kids to use our hands, cook, and tackle new tasks with enthusiasm. Traits I’ve benefited greatly from throughout my life.

I was fascinated by mathematics and by being able to prove things in a rigorous way.

J酶rgen Bang-Jensen, Professor Emeritus

As a child, Jørgen dreamed of becoming a professor of biology. He loved nature, catching lizards and snakes.

– When I was six, I caught spiders and fed them flies. Later, I started catching lizards, slow worms, and grass snakes, which I kept in my room—much to the horror of our cleaning lady, he says, laughing.

However, his interest in reptiles faded when his girlfriend (now his wife) put her foot down: 

– Lene thought they smelled bad—and that was the end of that!

Instead, mathematics and chemistry caught his attention, and he began studying at Odense University, as it was called back then.

– I was fascinated by mathematics and by being able to prove things in a rigorous way, he explains.

In high school, he had an inspiring math teacher who introduced him to more advanced topics like complex numbers. It was through this that he first encountered the name Bjarne Toft, who had written the notes they used on the subject (Bjarne is now also a beloved Emeritus at IMADA).

But French lessons were a different story.

– One day, the teacher asked me what a word meant in French, and I said I didn’t know. His response to the whole class was: ‘No, Jørgen, thick books could be written about what you don’t know!’

– Since this was otherwise a teacher I liked and remember fondly, I couldn’t resist sending him a flyer about my book Digraphs: Theory, Algorithms and Applications years later, with a note on the envelope saying: ‘Thick books can also be written about what I do know!’

J酶rgen as a baby with porridge all over him.

A pivotal fishing trip 

Jørgens career could have taken several directions. He considered working with mathematical aspects of spectroscopy but was told that would place him in an academic no-man’s-land (interdisciplinarity wasn’t always welcomed back then). Instead, he chose graph theory as his specialty—a decision made while sitting in his grandfather’s rowboat fishing.

It鈥檚 a bit like planting a tree and watching it grow.

J酶rgen Bang-Jensen, Professor Emeritus

– I chose to follow in Bjarne’s footsteps because he had sparked my interest in constructive proofs, and I could combine that with my interest in computer science, especially algorithms. It’s a choice I’ve never regretted, he says.

And Jørgen has good reason to be satisfied. His research has had remarkable international impact, particularly his 1988 discovery of "locally semicomplete digraphs," a class of graphs that has been the basis for over 100 scientific articles and several Ph.D. dissertations.

– It’s amazing to see how something I discovered almost by chance many years ago still lives on in others’ work. It’s a bit like planting a tree and watching it grow, he reflects, adding that he has also planted many actual trees in the large backyard of his summerhouse on Langeland, as gardening and outdoor life remain a big part of his leisure time.

J酶rgen Bang-Jensen and Rector Henrik Dam cutting a slice of brunsviger

The book on digraphs and cult status in China 

If there’s one piece of work Jørgen is particularly proud of, it’s the book , which he co-authored with , professor at Royal Holloway, University of London. -It was the first book to systematically cover the topic of digraphs.

– We gathered everything we knew about the field, and it has had enormous significance, he says. The book set a new standard for research in digraphs and made the field far more accessible to students and researchers alike.

– It’s incredible for me to think that something we wrote has become a foundational text studied in China, Canada, and many other places, he says.

The book is a symbol of what I鈥檝e always loved about research: gathering knowledge, creating something new, and making it easier for others to build on it.

J酶rgen Bang-Jensen, Professor Emeritus

Jørgen’s longstanding collaboration with Gutin and Anders Yeo (who was Jørgen’s Ph.D. student with Gutin as co-supervisor and who now also works at IMADA) has been a golden thread throughout his career, producing many important results in graph theory.

– The book is a symbol of what I’ve always loved about research: gathering knowledge, creating something new, and making it easier for others to build on it.

His work on digraphs has also earned him unexpected status in China, where he has held multiple online courses with up to 300 participants.

– Several of them have studied my book down to the smallest detail. It’s a rather peculiar feeling to have something of a cult status on the other side of the world, he says in a playful tone.

J酶rgen Bang Jensen and Gregory Gutin

Beer as motivation—and teaching without notes (though probably not in combination)

Jørgen has always been passionate about teaching and had a great role model in Bjarne Toft, who created ‘beer problems’ for students, with a Faxe Fad beer awarded for the best solution in front of the 500 students in the U55 auditorium. Jørgen himself once won such a prize, and he was so proud of his accomplishment that he nearly let the beer expire before drinking it. Although he hasn’t used exactly the same motivational methods in his own teaching, he has developed his own unique approach to capturing students’ attention.

J酶rgen has been a defining figure at IMADA for decades. With over 170 publications and more than 70 collaborators, his research has had a significant impact, but his contributions extend far beyond the academic realm.

Martin Svensson, Head of Department

In recent years, he has completely abandoned using notes during lectures, discovering that it forced him to have an even stronger overview.

– At one lecture years ago, a group of students amused themselves by counting how many times I took my reading glasses on and off. The result was 18 times during one lecture," he says, laughing.

– That made me adjust my teaching style, and I forced myself to have it all in my head instead of relying on notes—it’s actually improved my teaching a lot. While teaching, I learn alongside my students, and we reach conclusions together. The approach has also sharpened me in other contexts—I highly recommend it, he adds.

Her kan der st氓 en billedtekst ...

A giant steps down from the podium 

At the recent reception celebrating Jørgen’s long career and transition to emeritus status, it was clear that both his personality and his research will be remembered for many years.

Head of Department Martin Svensson expressed it as follows:

Jørgen has been a defining figure at IMADA for decades. With over 170 publications and more than 70 collaborators, his research has had a significant impact, but his contributions extend far beyond the academic realm. He has supervised an impressive number of students, many of whom have gone on to achieve high positions in Danish society.

His way of working—organized, solution-oriented, and always with a sharp sense of what truly matters—has been an inspiration. He has never been afraid to speak his mind, which we witnessed, for example, during a strategy seminar where he directly asked an external consultant what the actual purpose of the day's exercises was and whether he had considered the costs. That set a new agenda—and we never saw that consultant again.

We will miss his outstanding science, teaching, and engagement in institute life—as well as his ever-boundary-pushing humor. Fortunately, he continues as a professor emeritus, and I hope we will still benefit from his input (though perhaps with slightly fewer inappropriate jokes).


And his former mentor, Bjarne Toft, also had some memorable words, which, it seemed, brought a lump to the throat of more than a few in the audience:

Jørgen has been on a long journey in mathematics—and fortunately, it is not over yet. He came to IMADA 46 years ago as a student, and even back then, it was clear that he had a special talent. I clearly remember one of his early assignments from 1979, the infamous "beer problem," where he not only provided a theoretical calculation but also a down-to-earth argument. “WAW,” I thought! “Here is a future famous mathematician!” And I was not wrong.

Jørgen realized early on that digraphs were an underdeveloped area in graph theory, and he tackled it where no one else really had before. His work on locally semicomplete digraphs and the books Digraphs: Theory, Algorithms and Applications have not only filled a gap in research but opened up an entirely new world. The second edition of the book contains over 150 unsolved problems, demonstrating how much his work has shaped the field—and how much remains to be explored.

He has put IMADA on the world map and is today one of Denmark’s most internationally recognized mathematicians. Mathematical Reviews has registered 158 publications and over 2,100 citations, while Google counts more than 7,700 references to his work. And he has had as many as 73 different co-authors—for comparison, Harald Bohr had only six!

Although he has, as far as I know, never been to China, he is well-known there, not least through his remote teaching and supervision of Chinese researchers.

Personally, he has also meant a great deal to me. Over the years, we have organized countless international conferences together and attracted top researchers to Denmark—a great benefit for IMADA and for both of us.

Now, he is moving into the emeritus corridor, and that will not be bad at all—on the contrary. More time for family, more time for research and deep reflection, and more time for social relations. Welcome to the club!


J酶rgen Bang-Jensen in front of the board

Family life and future plans

But life isn’t only about mathematics. Jørgen has been with Lene, now his wife and the mother of their three children, since elementary school. Their youngest daughter, Victoria, has a mental disability, which has greatly influenced the family.

– It has taught us that life isn’t always about one’s own ambitions but about giving another person the best possible conditions, he says.

Jørgen shares how he and his wife have spent 34 years ensuring Victoria’s well-being and are still working to find the right group home for her.

– We can’t just place her somewhere we know she won’t thrive. We’ve spent a lifetime creating a good daily life for her, and that’s not something you just let go of. Fortunately, Victoria loves nature and animals as much as I do, so we have many wonderful experiences together," he explains.

Now, after a long academic life, it’s time to step back—at least partially.

– Many of my foreign colleagues doubt I’ll ever really stop. My wife, on the other hand, thinks I shouldn’t work too much without pay, so it’ll probably be somewhere in between, he says, noting that this balance is exactly the beauty of an emeritus position, allowing one to maintain a researcher’s life without all the obligations that steal time and focus from home.

The future holds travel, time with Lene, children, and grandchildren, restarting the vegetable garden at the summerhouse on Langeland, and more time for his great interest in wine and food.

– But I probably won’t be able to stop myself completely from finding new mathematical problems to solve," he finishes with a warm twinkle in his eye.

J酶rgen with his wife, Lene, and their daughter, Victoria.

 

Gray Hartley flanked by J酶rgen Bang-Jensen and his son Jonas.

 

Digraphs鈥攖he mathematics behind networks and optimization

Digraphs are a central part of discrete mathematics, specifically belonging to graph theory, a branch of mathematics that deals with network structures consisting of points (nodes) connected by lines (edges). When the connections have a specific direction, they are called directed graphs or digraphs.

Jørgen Bang’s research focuses on how digraphs can be used to solve complex problems in optimization and network analysis. One of his most significant contributions is the discovery of locally semicomplete digraphs, a class of digraphs that includes the well-known class of tournaments but is much larger and still shares many properties with them. Another notable result was achieved over 30 years ago with a Hungarian and an English collaborator. In the past 2-3 years, this result has proven to have several important practical applications, including scheduling communication in AI processors.

Digraphs play a crucial role in both mathematics and computer science and are used in a wide range of contexts—from transport planning and internet infrastructure to artificial intelligence and biological systems. Research in this field has great practical significance and forms the foundation for many of the technologies we use in everyday life.


B酶gerne om digrafer, som J酶rgen Bang-Jensen har skrevet sammen med Gregory Gutin, og som har givet ham kultstatus i Kina.
Editing was completed: 28.03.2025