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Ramsey Numbers Involving Graphs with Long Suspended Paths
Author(s) -
Burr S. A.
Publication year - 1981
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-24.3.405
Subject(s) - combinatorics , mathematics , graph , chromatic scale , ramsey's theorem , discrete mathematics
Let G be a graph with chromatic number χ and with t being the minimum number of points in any color class of any point‐coloring of G with χ colors. Let H be any connected graph and let H n be a graph on n points which is homeomorphic to H . It is proved that if n is large enough, the Ramsey number r ( G , H n ) satisfies r ( G , H n ) = (χ − l)( n −l) + t . It is also shown that for some G , no such result holds when H n is a star with n points.