Partitioning 3-edge-colored complete equi-bipartite graphs by monochromatic trees under a color degree condition.
Li, Xueliang, Liu, Fengxia (2008)
The Electronic Journal of Combinatorics [electronic only]
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Li, Xueliang, Liu, Fengxia (2008)
The Electronic Journal of Combinatorics [electronic only]
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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.
Collins, Karen L., Trenk, Ann N. (2006)
The Electronic Journal of Combinatorics [electronic only]
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Van Bussel, Frank (2002)
The Electronic Journal of Combinatorics [electronic only]
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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...
Bohdan Zelinka (1988)
Czechoslovak Mathematical Journal
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Bohdan Zelinka (1979)
Časopis pro pěstování matematiky
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