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Fractional, Circular, and Defective Coloring of Series‐Parallel Graphs
Author(s) -
Goddard Wayne,
Xu Honghai
Publication year - 2016
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.21868
Subject(s) - mathematics , combinatorics , chromatic scale , series (stratigraphy) , fractional coloring , series and parallel circuits , graph , graph coloring , list coloring , discrete mathematics , graph power , line graph , physics , quantum mechanics , biology , paleontology , voltage
In this note we consider colorings of series‐parallel graphs. Specifically, we provide bounds on their fractional and circular chromatic numbers and the defective version of these parameters. The main result is that the fractional chromatic number of any series‐parallel graph of odd girth k is exactly 2 k / ( k − 1 ) .