Open problems of the 33rd Workshop on Cycles and Colourings
J\'anos Bar\'at, Zden\v{e}k Dvo\v{r}\'ak, Penny Haxell, Franti\v{s}ek Kardo\v{s}, Borut Lu\v{z}ar, Alfr\'ed Onderko, Jozef Rajn\'ik, Roman Sot\'ak, Nikolay Ulyanov
TL;DR
This paper compiles open problems discussed at the 33rd Cycles and Colourings workshop, providing current context and references, serving as a resource for future research in graph theory.
Contribution
It documents and summarizes open problems from the 33rd workshop, including notes on their current status and relevant literature, facilitating ongoing research.
Findings
List of open problems in cycles and colourings
Notes on the current state of each problem
Bibliography of related research
Abstract
Since its beginnings, every Cycles and Colourings workshop holds one or two open problem sessions; this document contains the problems (together with notes regarding the current state of the art and related bibliography) presented by participants of the 33rd edition of the workshop which took place in Nov\'y Smokovec, Slovakia during August 31st - September 5th, 2025 (see the workshop webpage https://candc.upjs.sk).
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Taxonomy
TopicsQuasicrystal Structures and Properties · Aesthetic Perception and Analysis · Libraries and Information Services