Partitioning 2‐Edge‐Colored Ore‐Type Graphs by Monochromatic Cycles |
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| Authors: | János Barát Gábor N. Sárközy |
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| Affiliation: | 1. MTA‐ELTE GEOMETRIC AND ALGEBRAIC COMBINATORICS RESEARCH GROUP, BUDAPEST, HUNGARY;2. ALFRéD RéNYI INSTITUTE OF MATHEMATICS, HUNGARIAN ACADEMY OF SCIENCES, BUDAPEST, HUNGARY;3. COMPUTER SCIENCE DEPARTMENT, WORCESTER POLYTECHNIC INSTITUTE, WORCESTER, MA |
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| Abstract: | Consider a graph G on n vertices satisfying the following Ore‐type condition: for any two nonadjacent vertices x and y of G, we have  . We conjecture that if we color the edges of G with two colors then the vertex set of G can be partitioned to two vertex disjoint monochromatic cycles of distinct colors. In this article, we prove an asymptotic version of this conjecture. |
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| Keywords: | monochromatic partition Ore‐type graph |
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