منابع مشابه
Monochromatic s-t Paths in Edge-Colored Graphs
In this paper we consider an approach to solve the problem of finding monochromatic s-t paths in edge-colored graphs. This approach is based on constructing logical models for the problem. Algorithmic problems extensively investigated in bioinformatics (see e.g. [1] – [3]). In particular, there are a number of applications of different problems of finding paths. In this paper we consider the pr...
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For r ∈ N\{0} an r-edge coloring of a graph or hypergraph G = (V,E) is a map c : E → {0, . . . , r−1}. Extending results of Rado and answering questions of Rado, Gyárfás and Sárközy we prove that • every r-edge colored complete k-uniform hypergraph on N can be partitioned into r monochromatic tight paths with distinct colors (a tight path in a kuniform hypergraph is a sequence of distinct verti...
متن کاملPartitioning edge-2-colored graphs by monochromatic paths and cycles
We present results on partitioning the vertices of 2-edge-colored graphs into monochromatic paths and cycles. We prove asymptotically the two-color case of a conjecture of Sárközy: the vertex set of every 2-edge-colored graph can be partitioned into at most 2α(G) monochromatic cycles, where α(G) denotes the independence number of G. Another direction, emerged recently from a conjecture of Schel...
متن کاملPartitioning 2-edge-colored graphs by monochromatic paths and cycles
We present results on partitioning the vertices of 2-edge-colored graphs into monochromatic paths and cycles. We prove asymptotically the two-color case of a conjecture of Sárközy: the vertex set of every 2-edge-colored graph can be partitioned into at most 2α(G) monochromatic cycles, where α(G) denotes the independence number of G. Another direction, emerged recently from a conjecture of Schel...
متن کاملMonochromatic cycle partitions of edge-colored graphs
In this article we study the monochromatic cycle partition problem for non-complete graphs. We consider graphs with a given independence number (G)= . Generalizing a classical conjecture of Erd” os, Gyárfás and Pyber, we conjecture that if we r -color the edges of a graph G with (G)= , then the vertex set of G can be partitioned into at most r vertex disjoint monochromatic cycles. In the direct...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1972
ISSN: 0095-8956
DOI: 10.1016/0095-8956(72)90009-3