A tight lower bound on the size of planar permutation networks

MacGillivary and Seyffarth [G. MacGillivray, K. Seyffarth, Domination numbers of planar graphs, J. Graph Theory 22 (1996) 213-229] proved that planar graphs of diameter two have domination number at most three. Goddard and Henning [W. Goddard, M.A. ...

Given an edge coloring F of a graph G, a vertex coloring of G is adapted to F if no color appears at the same time on an edge and on its two endpoints. If for some integer k, a graph G is such that given any list assignment L to the vertices of G, with |...

Let G=(V,E) be a graph. A proper vertex coloring of G is acyclic if G contains no bicolored cycle. Namely, every cycle of G must be colored with at least three colors. G is acyclically L-list colorable if for a given list assignment L={L(v):v@?V}, there ...