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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Watkins, Mark E., Zhou, Xiangqian (2007)
The Electronic Journal of Combinatorics [electronic only]
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Lang, Wolfdieter (2009)
Journal of Integer Sequences [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...
Yan, Sherry H.F. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Picollelli, Michael E. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Bohdan Zelinka (1991)
Mathematica Bohemica
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Two types of a distance between isomorphism classes of graphs are adapted for rooted trees.
Xueliang Li, Ingo Schiermeyer, Kang Yang, Yan Zhao (2015)
Discussiones Mathematicae Graph Theory
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Let G = (V (G),E(G)) be a nontrivial connected graph of order n with an edge-coloring c : E(G) → {1, 2, . . . , q}, q ∈ N, where adjacent edges may be colored the same. A tree T in G is a rainbow tree if no two edges of T receive the same color. For a vertex set S ⊆ V (G), a tree connecting S in G is called an S-tree. The minimum number of colors that are needed in an edge-coloring of G such that there is a rainbow S-tree for each k-subset S of V (G) is called the k-rainbow index of...
Constantine, Gregory M., Buliga, Marius G. (2004)
International Journal of Mathematics and Mathematical Sciences
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Lily Chen, Xueliang Li, Kang Yang, Yan Zhao (2015)
Discussiones Mathematicae Graph Theory
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Let G be a nontrivial connected graph with an edge-coloring c : E(G) → {1, 2, . . . , q}, q ∈ ℕ, where adjacent edges may be colored the same. A tree T in G is a rainbow tree if no two edges of T receive the same color. For a vertex subset S ⊆ V (G), a tree that connects S in G is called an S-tree. The minimum number of colors that are needed in an edge-coloring of G such that there is a rainbow S-tree for each k-subset S of V (G) is called the k-rainbow index of G, denoted by rxk(G)....
Seo, Seunghyun (2005)
The Electronic Journal of Combinatorics [electronic only]
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