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Graph classes characterized both by forbidden subgraphs and degree sequences

✍ Scribed by Michael D. Barrus; Mohit Kumbhat; Stephen G. Hartke


Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
198 KB
Volume
57
Category
Article
ISSN
0364-9024

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✦ Synopsis


Abstract

Given a set ${\cal F}$ of graphs, a graph G is ${\cal F}$‐free if G does not contain any member of ${\cal F}$ as an induced subgraph. We say that ${\cal F}$ is a degree‐sequence‐forcing set if, for each graph G in the class ${\cal C}$ of ${\cal F}$‐free graphs, every realization of the degree sequence of G is also in ${\cal C}$. We give a complete characterization of the degree‐sequence‐forcing sets ${\cal F}$ when ${\cal F}$ has cardinality at most two. © 2007 Wiley Periodicals, Inc. J Graph Theory 57: 131–148, 2008