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Displaying similar documents to “Distinguishability of locally finite trees.”

Parity vertex colorings of binomial trees

Petr Gregor, Riste Škrekovski (2012)

Discussiones Mathematicae Graph Theory

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We show for every k ≥ 1 that the binomial tree of order 3k has a vertex-coloring with 2k+1 colors such that every path contains some color odd number of times. This disproves a conjecture from [1] asserting that for every tree T the minimal number of colors in a such coloring of T is at least the vertex ranking number of T minus one.

Minimum vertex ranking spanning tree problem for chordal and proper interval graphs

Dariusz Dereniowski (2009)

Discussiones Mathematicae Graph Theory

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A vertex k-ranking of a simple graph is a coloring of its vertices with k colors in such a way that each path connecting two vertices of the same color contains a vertex with a bigger color. Consider the minimum vertex ranking spanning tree (MVRST) problem where the goal is to find a spanning tree of a given graph G which has a vertex ranking using the minimal number of colors over vertex rankings of all spanning trees of G. K. Miyata et al. proved in [NP-hardness proof and an approximation...