Rao's degree sequence conjecture

Maria Chudnovsky; Paul Seymour

doi:10.1016/j.jctb.2013.12.003

Rao's degree sequence conjecture

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Let us say two (simple) graphs G, G^' are degree-equivalent if they have the same vertex set, and for every vertex, its degrees in G and in G^' are equal. In the early 1980's, S.B. Rao made the conjecture that in any infinite set of graphs, there exist two of them, say G and H, such that H is isomorphic to an induced subgraph of some graph that is degree-equivalent to G. We prove this conjecture.

Original language	English (US)
Pages (from-to)	44-92
Number of pages	49
Journal	Journal of Combinatorial Theory. Series B
Volume	105
Issue number	1
DOIs	https://doi.org/10.1016/j.jctb.2013.12.003
State	Published - 2014

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Keywords

Graph structure theory
Induced subgraph
Well-quasi-ordering

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10.1016/j.jctb.2013.12.003

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AU - Seymour, Paul

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AB - Let us say two (simple) graphs G, G' are degree-equivalent if they have the same vertex set, and for every vertex, its degrees in G and in G' are equal. In the early 1980's, S.B. Rao made the conjecture that in any infinite set of graphs, there exist two of them, say G and H, such that H is isomorphic to an induced subgraph of some graph that is degree-equivalent to G. We prove this conjecture.

KW - Graph structure theory

KW - Induced subgraph

KW - Well-quasi-ordering

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Rao's degree sequence conjecture

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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