Herbert Fleischner (1944–2025)

Herbert Fleischner, who passed away on October 7, 2025, in Vienna, was a mathematician whose work shaped our understanding of graph theory. Born in London on January 29, 1944, he moved to Vienna with his parents in 1946 and remained connected to the city throughout his life, even as his career took him across continents.

Herbert studied mathematics and physics at the University of Vienna under Nikolaus Hofreiter and Edmund Hlawka, earning his PhD in 1968. His dissertation focused on Eulerian and Hamiltonian graphs, topics that would define his research for decades. While Hlawka was his official supervisor, Herbert Izbicki provided the actual guidance, being a graph theorist himself.

His most influential contribution came early in his career. In 1971, he submitted a proof showing that the square of every two-connected graph contains a Hamiltonian cycle. Published in 1974, this result became known as Fleischner's theorem and remains a cornerstone in graph theory. The elegance of the statement, which is simple to understand yet challenging to prove, captured something essential about the structure of graphs.

Another milestone in his research was solving Paul Erdős's "Cycle plus Triangles" problem, work he accomplished in collaboration with Michael Stiebitz. That paper appeared in 1992 in a special issue honoring Julius Petersen. His Erdős number was 2.

Herbert's career path was anything but conventional. After positions at SUNY Binghamton and a year at the Institute for Advanced Study in Princeton, he spent most of his professional life at the Austrian Academy of Sciences, from 1973 to 2002. However, he was always on the move, traveling to Memphis, MIT, and making multiple stays in Canada, as well as regularly visiting Texas A&M. In 2003, Herbert joined TU Wien, where he continued his research as the PI of projects from the Austrian Science Funds (FWF) as part of what is now the Algorithms and Complexity Group at the Institute of Logic and Computation. In total, Herbert secured four grants from the Austrian Science Fund (FWF), one while at the Austrian Academy of Sciences, where I collaborated as a PhD student, and three at TU Wien, in collaboration with my colleague Günther Raidl. Herbert worked on graph theoretical problems until his last days.

What set Herbert apart was his commitment to mathematics education in developing countries. From the late 1990s to 2012, he worked extensively with the University of Zimbabwe, serving as the main lecturer and project coordinator for an M.Sc. program in academic staff development (1997-1999, sponsored by UNESCO and the Austrian Development Cooperation), and subsequently making regular visits for teaching and supervision through 2012. He did similar work at the University of Dar es Salaam in Tanzania from 2003 to 2009. From 2001 to 2007, he chaired the Committee for Developing Countries of the European Mathematical Society, working to strengthen mathematical research and education where it was needed most.

He supervised nine PhD students. I was fortunate to be among them. Herbert was genuinely open to ideas and topics. Some of my best memories are standing with him in front of a blackboard, working through an argument together. He'd draw a graph, we'd discuss where it might lead, and he'd push for thoroughness: every case would be considered, and every detail would be checked. Those sessions taught me what mathematical thinking, where intuition meets precision, actually looks like.

He organized workshops on the Matthews-Sumner Conjecture with Zdeněk Ryjáček in the Czech Republic, bringing together researchers who shared his passion for cycle-related problems in graphs.

Herbert wrote two volumes on Eulerian graphs, published in 1990 and 1991, that became standard references. They were translated into Russian and Chinese, a testament to their lasting value. Over his career, he published more than 90 papers. He also found an unexpected connection between mathematics and art through his friendship with painter Robert Lettner. They collaborated on a series called "mutations," where mathematical graphs were transformed into paintings.

Herbert spoke German, English, and Russian fluently. Beyond his professional achievements, he raised his son, Michael, born in 1974, as a single father during a time when this was uncommon. Later in life, he found happiness with his wife Renata, whom he married in 2005.

Herbert Fleischner spent his life building structures: mathematical structures in graph theory, educational structures in developing countries, collaborative structures across continents. He understood that mathematics isn't just about theorems; it's about creating communities where ideas can grow.

We'll miss him.

Stefan Szeider

Algorithms and Complexity Group, TU Wien