Erdos-Gyárfás conjecture for cubic planar graphs

Christopher Carl Heckman; Roi Krakovski

doi:10.37236/3252

Erdos-Gyárfás conjecture for cubic planar graphs

Christopher Carl Heckman, Roi Krakovski

Department of Mathematics

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

9 Scopus citations

Abstract

In 1995, Paul Erdo{double acute}s and András Gyárfás conjectured that for every graph of minimum degree at least 3, there exists a non-negative integer m such that G contains a simple cycle of length 2^m. In this paper, we prove that the conjecture holds for 3-connected cubic planar graphs. The proof is long, computer-based in parts, and employs the Discharging Method in a novel way.

Original language	English
Journal	Electronic Journal of Combinatorics
Volume	20
Issue number	2
DOIs	https://doi.org/10.37236/3252
State	Published - 9 Apr 2013

Keywords

Cubic planar graphs
Cycles of prescribed lengths
ErdoO{double acute}s-Gyárfás Conjecture

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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10.37236/3252

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abstract = "In 1995, Paul Erdo\{double acute\}s and Andr{\'a}s Gy{\'a}rf{\'a}s conjectured that for every graph of minimum degree at least 3, there exists a non-negative integer m such that G contains a simple cycle of length 2m. In this paper, we prove that the conjecture holds for 3-connected cubic planar graphs. The proof is long, computer-based in parts, and employs the Discharging Method in a novel way.",

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AU - Krakovski, Roi

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AB - In 1995, Paul Erdo{double acute}s and András Gyárfás conjectured that for every graph of minimum degree at least 3, there exists a non-negative integer m such that G contains a simple cycle of length 2m. In this paper, we prove that the conjecture holds for 3-connected cubic planar graphs. The proof is long, computer-based in parts, and employs the Discharging Method in a novel way.

KW - Cubic planar graphs

KW - Cycles of prescribed lengths

KW - ErdoO{double acute}s-Gyárfás Conjecture

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Erdos-Gyárfás conjecture for cubic planar graphs

Abstract

Keywords

ASJC Scopus subject areas

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