TY - JOUR

T1 - Radius two trees specify χ‐bounded classes

AU - Kierstead, Henry

AU - Penrice, S. G.

PY - 1994/3

Y1 - 1994/3

N2 - A class of graphs χ is said to be χ‐bounded, with χ‐binding function f, if for all G ϵ Γ, χ (G) ≦ f (ω(G)), where χ(G) is the chromatic number of G and ω(G) is the clique number of G. It has been conjectured that for every tree T, the class of graphs that do not induce T is χ‐bounded. We show that this is true in the case where T is a tree of radius two.

AB - A class of graphs χ is said to be χ‐bounded, with χ‐binding function f, if for all G ϵ Γ, χ (G) ≦ f (ω(G)), where χ(G) is the chromatic number of G and ω(G) is the clique number of G. It has been conjectured that for every tree T, the class of graphs that do not induce T is χ‐bounded. We show that this is true in the case where T is a tree of radius two.

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U2 - 10.1002/jgt.3190180203

DO - 10.1002/jgt.3190180203

M3 - Article

AN - SCOPUS:84987477084

SN - 0364-9024

VL - 18

SP - 119

EP - 129

JO - Journal of Graph Theory

JF - Journal of Graph Theory

IS - 2

ER -