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The Ramsey numbers of two sets of cycles
Author(s) -
Wang Longqin,
Chen Yaojun
Publication year - 2021
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22564
Subject(s) - ramsey's theorem , combinatorics , mathematics , conjecture , graph , integer (computer science) , discrete mathematics , computer science , programming language
For two given sets C 1 and C 2 of cycles, the Ramsey number R ( C 1 , C 2 ) is the smallest integer N such that for any graph G on N vertices, either G contains a cycle from C 1 or G ¯ contains a cycle from C 2 . In this paper, we determine all Ramsey numbers R ( C 1 , C 2 ) , which confirms a conjecture due to Hansson, and extends the well‐known Ramsey numbers for two cycles.