The circumference of a graph with no \(K_{3,t}\)-minor
type: Item
instance of: scholarly article
title: The circumference of a graph with no \(K_{3,t}\)-minor
zbMATH Open document ID: 1111.05052
author: Guantao Chen
author: Laura Sheppardson
author: Xingxing Yu
author: Wenan Zang
published in: Journal of Combinatorial Theory. Series B
publication date: 2007-01-16T00:00:00Z
review text: Let \(t\) be any integer such that \(t\geq 3\). The authors show that if \(G\) is a 3-connected graph with \(n\) nodes that contains no \(K_{3,t}\)-minors, then \(G\) has a cycle of length at least \(n^{r(t)}\), where \(r(t)= \log_{8t}(t-1)^2\); and if \(G\) is a 2-connected graph with \(n\) nodes that contains no \(K_{2,t}\)-minors, then \(G\) has a cycle of length at least \(n/t^{t-1}\).
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 5116329
zbMATH Keywords: cycle
zbMATH Keywords: path
zbMATH Keywords: connectivity
reviewed by: J. W. Moon
MaRDI profile type: Publication
full work available at URL: j.jctb.2006.02.006
OpenAlex ID: W2148375186
cites work: \(K_{a,k}\) minors in graphs of bounded tree-width
cites work: Long cycles in graphs on a fixed surface
cites work: Long cycles in 3-connected graphs
cites work: Convex programming and circumference of 3-connected graphs of low genus
cites work: Polytopes, graphs, and complexes
cites work: Shortness exponents of families of graphs
cites work: The smallest non-Hamiltonian 3-connected cubic planar graphs have 38 vertices
cites work: Longest cycles in 3-connected planar graphs
cites work: Q3834063
cites work: Simple paths on polyhedra
cites work: Q5678882
cites work: Typical subgraphs of 3- and 4-connected graphs
cites work: Long cycles in 3‐connected graphs in orientable surfaces
cites work: 4-connected projective planar graphs are Hamiltonian
cites work: Five-connected toroidal graphs are Hamiltonian
cites work: Hamilton paths in toroidal graphs
cites work: A theorem on paths in planar graphs
cites work: A Theorem on Planar Graphs
cites work: Disjoint paths, planarizing cycles, and spanning walks
DOI: 10.1016/J.JCTB.2006.02.006
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description: scientific article; zbMATH DE number 5116329