Graph colouring remains a central topic in graph theory, providing the mathematical framework for assigning colours to the elements of a graph under specific constraints. In particular, the colouring ...
If true, the following conjecture of Thomassen [Th81] is a planarity criterion for a special class of graphs that involves only K 5. Recall that a planar graph on n vertices contains at most 3n-6 ...
The July 2002 Problem of the month is related to an old conjecture of Albertson and Berman [1]: Borodin's theorem about acyclic 5-colorability of planar graphs implies that k/n is at least 2/5.
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