Ramsey and Gallai-Ramsey Numbers for Two Classes of Unicyclic Graphs
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DOI: 10.1007/s00373-020-02248-8
Abstract: Given a graph G and a positive integer k , define the Gallai-Ramsey number to be the minimum number of vertices n such that any k -edge coloring of $$K_n$$ K n contains either a… read more here.
Keywords: classes unicyclic; unicyclic graphs; two classes; ramsey ... See more keywords
Star-Critical Ramsey Numbers of Cycles Versus Wheels
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DOI: 10.1007/s00373-021-02343-4
Abstract: For two graphs $$G_1$$ and $$G_2$$ , the star-critical Ramsey number $$r_*(G_1,G_2)$$ is the minimum integer k such that any red/blue edge-coloring of $$K_{r-1}\sqcup K_{1,k}$$ contains a red copy of $$G_1$$ or a blue copy… read more here.
Keywords: cycles versus; numbers cycles; critical ramsey; ramsey ... See more keywords
Lower bounds for Ramsey numbers as a statistical physics problem
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DOI: 10.1088/1742-5468/ac5cb3
Abstract: Ramsey’s theorem, concerning the guarantee of certain monochromatic patterns in large enough edge-coloured complete graphs, is a fundamental result in combinatorial mathematics. In this work, we highlight the connection between this abstract setting and a… read more here.
Keywords: ramsey numbers; statistical physics; bounds ramsey; physics ... See more keywords