On the hamiltonicity of line graphs of locally finite, 6-edge-connected graphs

Authors:
Richard C. Brewster;Daryl Funk
Affiliations:
Department of Mathematics and Statistics, Thompson Rivers University, Kamloops, BC, Canada;Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada
Venue:
Journal of Graph Theory
Year:
2012

Citing 14
Cited 0

On Infinite Cycles I

Combinatorica
On Infinite Cycles II

Combinatorica
Topological paths, cycles and spanning trees in infinite graphs

European Journal of Combinatorics - Special issue: Topological graph theory
The Cycle Space of an Infinite Graph

Combinatorics, Probability and Computing
The cycle space of a 3-connected locally finite graph is generated by its finite and infinite peripheral circuits

Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
MacLane's planarity criterion for locally finite graphs

Journal of Combinatorial Theory Series B
Graphs embedded in the plane with a bounded number of accumulation points

Journal of Graph Theory
Cycle-cocycle partitions and faithful cycle covers for locally finite graphs

Journal of Graph Theory
Menger's theorem for infinite graphs with ends

Journal of Graph Theory
On end degrees and infinite cycles in locally finite graphs

Combinatorica
Cycle spaces in topological spaces

Journal of Graph Theory
The bond and cycle spaces of an infinite graph

Journal of Graph Theory
Hamilton Cycles in Planar Locally Finite Graphs

SIAM Journal on Discrete Mathematics
Hamilton circles in infinite planar graphs

Journal of Combinatorial Theory Series B

Quantified Score

Hi-index	0.00

Visualization

Abstract

The topological approach to the study of infinite graphs of Diestel and KÜhn has enabled several results on Hamilton cycles in finite graphs to be extended to locally finite graphs. We consider the result that the line graph of a finite 4-edge-connected graph is hamiltonian. We prove a weaker version of this result for infinite graphs: The line graph of locally finite, 6-edge-connected graph with a finite number of ends, each of which is thin, is hamiltonian. © 2012 Wiley Periodicals, Inc.