Displaying similar documents to “ k -colored point-set embeddability of outerplanar graphs.”

Regulated buildups of 3-configurations

Václav J. Havel (1994)

Archivum Mathematicum

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We deal with two types of buildups of 3-configurations: a generating buildup over a given edge set and a regulated one (according to maximal relative degrees of vertices over a penetrable set of vertices). Then we take account to minimal generating edge sets, i.e., to edge bases. We also deduce the fundamental relation between the numbers of all vertices, of all edges from edge basis and of all terminal elements. The topic is parallel to a certain part of Belousov' “Configurations...

Adjacent vertex distinguishing edge colorings of the direct product of a regular graph by a path or a cycle

Laura Frigerio, Federico Lastaria, Norma Zagaglia Salvi (2011)

Discussiones Mathematicae Graph Theory

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In this paper we investigate the minimum number of colors required for a proper edge coloring of a finite, undirected, regular graph G in which no two adjacent vertices are incident to edges colored with the same set of colors. In particular, we study this parameter in relation to the direct product of G by a path or a cycle.

Adjacent vertex distinguishing edge-colorings of planar graphs with girth at least six

Yuehua Bu, Ko-Wei Lih, Weifan Wang (2011)

Discussiones Mathematicae Graph Theory

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An adjacent vertex distinguishing edge-coloring of a graph G is a proper edge-coloring o G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing edge-coloring of G is denoted by χ'ₐ(G). We prove that χ'ₐ(G) is at most the maximum degree plus 2 if G is a planar graph without isolated edges whose girth is at least 6. This gives new evidence to a conjecture proposed in [Z. Zhang, L. Liu,...