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Anti-Ramsey numbers of graphs with some decomposition family sequences
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abstract
For a given graph $H$, the anti-Ramsey number of $H$ is the maximum number of colors in an edge-coloring of a complete graph which does not contain a rainbow copy of $H$. In this paper, we extend the decomposition family of graphs to the decomposition family sequence of graphs and show that $K_5$ is determined by its decomposition family sequence. Based on this new graph notation, we determine the anti-Ramsey numbers for new families of graphs, including the Petersen graph, vertex-disjoint union of cliques, etc., and characterize the extremal colorings.
Forward citations
Cited by 2 Pith papers
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Anti-Ramsey number of intersecting cliques
The paper states ar(n,F_{k+1,r}) = ex(n,F_{k,r}) + 2 for large n, but the proof is incomplete as written.
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New Bounds on the Anti-Ramsey Number of Independent Triangles
The exact anti-Ramsey number for t+2 vertex-disjoint rainbow triangles in K_n is shown to hold for all n ≥ 15t+57, improving the previous quadratic threshold.
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