Partitioning by Monochromatic Trees
نویسندگان
چکیده
منابع مشابه
Partitioning 3-Edge-Colored Complete Equi-Bipartite Graphs by Monochromatic Trees under a Color Degree Condition
The monochromatic tree partition number of an r-edge-colored graph G, denoted by tr(G), is the minimum integer k such that whenever the edges of G are colored with r colors, the vertices of G can be covered by at most k vertex-disjoint monochromatic trees. In general, to determine this number is very difficult. For 2edge-colored complete multipartite graph, Kaneko, Kano, and Suzuki gave the exa...
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Let G be an edge-colored graph. We show in this paper that it is NP-hard to find the minimum number of vertex disjoint monochromatic trees which cover the vertices of the graph G. We also show that there is no constant factor approximation algorithm for the problem unless P = NP. The same results hold for the problem of finding the minimum number of vertex disjoint monochromatic cycles (paths, ...
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The tree partition number of an r-edge-colored graph G, denoted by tr(G), is the minimum number k such that whenever the edges of G are colored with r colors, the vertices of G can be covered by at most k vertex-disjoint monochromatic trees. We determine t2(K(n1, n2, . . . , nk)) of the complete k-partite graph K(n1, n2, . . . , nk). In particular, we prove that t2(K(n,m)) = (m − 2)/2n + 2, whe...
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In this paper we consider the problem of partitioning complete multipartite graphs with edges colored by 2 colors into the minimum number of vertex disjoint monochromatic cycles, paths and trees, respectively. For general graphs we simply address the decision version of these three problems the 2-PGMC, 2-PGMP and 2-PGMT problems, respectively. We show that both 2-PGMC and 2-PGMP problems are NP...
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Consider a graph G on n vertices satisfying the following Ore-type condition: for any two non-adjacent vertices x and y of G, we have deg(x)+deg(y) > 3n/2. We conjecture that if we color the edges of G with 2 colors then the vertex set of G can be partitioned to two vertex disjoint monochromatic cycles of distinct colors. In this paper we prove an asymptotic version of this conjecture. 1 Backgr...
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عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 68 شماره
صفحات -
تاریخ انتشار 1996