This research topic explores the theoretical foundations and practical applications of graph labeling and coloring problems, both of which are central to modern combinatorics and computer science.

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 ...

Conjecture 1: For every surface S there is an integer w such that every graph G embedded in S has a set U of vertices such that |U| w and G - U is 5-choosable. Conjecture 2: For every surface S there ...