Closing the gap on path-kipas Ramsey numbers

Binlong Li, Yanbo Zhang, Halina Bielak, Haitze J. Broersma, Premysl Holub

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    Abstract

    Given two graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer N such that, for any graph G of order N, either G1 is a subgraph of G, or G2 is a subgraph of the complement of G. Let Pn denote a path of order n and K^m a kipas of order m + 1, i.e., the graph obtained from a Pm by adding one new vertex v and edges from v to all vertices of the Pm. We close the gap in existing knowledge on exact values of the Ramsey numbers R(Pn,K^m) by determining the exact values for the remaining open cases.
    Original languageUndefined
    Pages (from-to)3.21
    Number of pages8
    JournalElectronic journal of combinatorics
    Volume22
    Issue number3
    Publication statusPublished - 14 Aug 2015

    Keywords

    • MSC-05C
    • EWI-26317
    • Ramsey number
    • IR-98275
    • Path
    • METIS-314968
    • Kipas

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