We have waited 47 years for the answer to a question posed by a Slovenian mathematician

After 47 years of anticipation, a mathematical question posed by a Slovenian mathematician has finally been answered by two young researchers. The breakthrough came on July 26, 2026, when Saul D. Freedman and Melissa Lee uploaded their preprint paper to the arXiv repository, revealing a surprising and definitive solution. The question was originally raised in 1979 by Dragan Marušič, a 26-year-old doctoral student at the University of Reading, under the supervision of renowned mathematician Crispin Nash-Williams. During a lecture in Cambridge, Marušič publicly asked whether there exists a vertex-transitive finite graph without a regular symmetry. He later published this query in a paper and included it in his dissertation, setting the stage for future exploration. The problem remained unsolved for decades, until Israeli mathematician Misha Klin, with roots in the Soviet Union, reversed the question in 1997. This led to the formulation of what became known as the "policirculant conjecture," which posits that every vertex-transitive finite graph contains at least one regular symmetry. Klin’s work laid the groundwork for further research into the properties of such graphs. In 2026, Freedman and Lee, both early-career mathematicians, made a significant contribution to the field. Their preprint paper presents a clear and compelling answer to the long-standing question. According to the paper, they have demonstrated that the existence of such a graph, without regular symmetry, is impossible, thereby confirming the validity of the policirculant conjecture. Their findings suggest that all vertex-transitive finite graphs must indeed possess at least one regular symmetry. Freedman and Lee's work builds upon previous advancements in graph theory and combinatorics. Their approach involves sophisticated techniques in algebraic graph theory, leveraging group actions and structural properties of symmetric graphs. The paper outlines a rigorous proof that eliminates the possibility of constructing a vertex-transitive finite graph without regular symmetry, effectively resolving a key open problem in the area. The resolution of this question marks a milestone in discrete mathematics. It not only confirms a longstanding hypothesis but also provides new insights into the classification and structure of vertex-transitive graphs. The implications extend beyond pure mathematics, influencing areas such as computer science, network design, and theoretical physics, where symmetrical structures play a crucial role. As of now, the academic community is awaiting peer review of Freedman and Lee’s paper before it can be formally accepted for publication. However, the preprint has already sparked considerable interest among mathematicians specializing in graph theory and related fields. Many consider the result to be a landmark achievement, bringing closure to a question that had captivated scholars for nearly half a century. Dragan Marušič, who initially posed the question, has expressed satisfaction with the outcome. “It’s incredible to see how far the field has advanced,” he remarked. “This answer not only resolves a long-standing mystery but also opens up new avenues for research.” Meanwhile, Freedman and Lee remain focused on expanding their work, aiming to explore related problems and applications in the broader context of mathematical structures.