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The circular chromatic number of series‐parallel graphs with large girth
Author(s) -
Chien Chihyun,
Zhu Xuding
Publication year - 2000
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/(sici)1097-0118(200004)33:4<185::aid-jgt1>3.0.co;2-n
Subject(s) - combinatorics , girth (graph theory) , mathematics , graph , series (stratigraphy) , triangle free graph , odd graph , chromatic scale , discrete mathematics , foster graph , graph power , 1 planar graph , chordal graph , line graph , paleontology , biology
It was proved by Hell and Zhu that, if G is a series‐parallel graph of girth at least 2⌊(3 k − 1)/2⌋, then χ c ( G ) ≤ 4 k /(2 k − 1). In this article, we prove that the girth requirement is sharp, i.e., for any k ≥ 2, there is a series‐parallel graph G of girth 2⌊(3 k − 1)/2⌋ − 1 such that χ c ( G ) > 4 k /(2 k − 1). © 2000 John Wiley & Sons, Inc. J Graph Theory 33: 185–198, 2000