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Density of the circular chromatic numbers of series‐parallel graphs
Author(s) -
Pan Zhishi,
Zhu Xuding
Publication year - 2004
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.10171
Subject(s) - combinatorics , mathematics , chromatic scale , graph , rational number , series and parallel circuits , series (stratigraphy) , windmill graph , discrete mathematics , friendship graph , graph power , line graph , paleontology , physics , quantum mechanics , voltage , biology
Suppose G is a series‐parallel graph. It was proved in 3 that either χ c ( G ) = 3 or χ c ( G ) ≤ 8/3. So none of the rationals in the interval (8/3, 3) is the circular chromatic number of a series‐parallel graph. This paper proves that for every rational r ∈ [2, 8/3] ∪ {3} there exists a series‐parallel graph G with χ c ( G ) = r . © 2004 Wiley Periodicals, Inc. J Graph Theory 46:57–68, 2004
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