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A note on Ramsey size‐linear graphs
Author(s) -
Balister P.N.,
Schelp R.H.,
Simonovits M.
Publication year - 2002
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.10001
Subject(s) - combinatorics , ramsey's theorem , mathematics , graph , discrete mathematics , ramsey theory
We show that if G is a Ramsey size‐linear graph and x,y ∈ V ( G ) then if we add a sufficiently long path between x and y we obtain a new Ramsey size‐linear graph. As a consequence we show that if G is any graph such that every cycle in G contains at least four consecutive vertices of degree 2 then G is Ramsey size‐linear. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 1–5, 2002