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.
UR - http://www.scopus.com/inward/record.url?scp=84987477084&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84987477084&partnerID=8YFLogxK
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 -