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Journals and Conferences
In FOCS 2002, Even et al. showed that any set of n discs in the plane can be Conflict-Free colored with a total of at most O(log n) colors. That is, it can be colored with O(log n) colors such that for any (covered) point p there is some disc whose color is distinct from all other colors of discs containing p. They also showed that this bound is… (More)
It is proved that the vertices of a cubic bipartite plane graph can be colored with four colors such that each face meets all four colors. This is tight, since any such graph contains at least six faces of size four.
Graphs distinguished by Kr -minor prohibition limited to subgraphs induced by circuits have chromatic number bounded by a function f (r); precise bounds on f (r) are unknown. If minor prohibition is limited to subgraphs induced by simple paths instead of circuits, then for certain forbidden configurations, we reach tight estimates. A graph whose simple… (More)