Approximating Longest Cycles in Graphs with Bounded Degrees

Approximating Longest Cycles in Graphs with Bounded Degrees

Jackson and Wormald conjecture that if $G$ is a 3-connected $n$-vertex graph with maximum degree $d\ge 4$, then $G$ has a cycle of length $\Omega(n^{\log_{d-1}2})$. We show that this conjecture holds when $d-1$ is replaced by $\max\{64,4d+1\}$. Our proof implies a cubic algorithm for finding such a...

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Veröffentlicht in:SIAM journal on computing 2006-01, Vol.36 (3), p.635-656
Hauptverfasser: Chen, Guantao, Gao, Zhicheng, Yu, Xingxing, Zang, Wenan
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Applied mathematics
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Decomposition
Graphs
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Gao, Zhicheng
Yu, Xingxing
Zang, Wenan
description Jackson and Wormald conjecture that if $G$ is a 3-connected $n$-vertex graph with maximum degree $d\ge 4$, then $G$ has a cycle of length $\Omega(n^{\log_{d-1}2})$. We show that this conjecture holds when $d-1$ is replaced by $\max\{64,4d+1\}$. Our proof implies a cubic algorithm for finding such a cycle.
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subjects Algorithms
Applied mathematics
Approximation
Combinatorics
Decomposition
Graphs
title Approximating Longest Cycles in Graphs with Bounded Degrees
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