Coloring complexes and arrangements

Steingrimsson’s coloring complex and Jonsson’s unipolar complex are interpreted in terms of hyperplane arrangements. This viewpoint leads to short proofs that all coloring complexes and a large class of unipolar complexes have convex ear decompositions. These convex ear decompositions impose strong...

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Bibliographic Details
Published inJournal of algebraic combinatorics Vol. 27; no. 2; pp. 205 - 214
Main Authors Hersh, Patricia, Swartz, Ed
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.04.2008
Subjects
Combinatorics
Computer Science
Convex and Discrete Geometry
Group Theory and Generalizations
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Chromatic polynomial
Coloring complex
Convex ear decomposition
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Summary:Steingrimsson’s coloring complex and Jonsson’s unipolar complex are interpreted in terms of hyperplane arrangements. This viewpoint leads to short proofs that all coloring complexes and a large class of unipolar complexes have convex ear decompositions. These convex ear decompositions impose strong new restrictions on the chromatic polynomials of all finite graphs. Similar results are obtained for characteristic polynomials of submatroids of type ℬ n arrangements.
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-007-0086-z