Cycle spectra of Hamiltonian graphs

Authors:
Kevin G. Milans;Florian Pfender;Dieter Rautenbach;Friedrich Regen;Douglas B. West
Affiliations:
Mathematics Dept., University of South Carolina, USA;Institut für Mathematik, Universität Rostock, Rostock, Germany;Institut für Optimierung und Operations Research, Universität Ulm, Ulm, Germany;Institut für Optimierung und Operations Research, Universität Ulm, Ulm, Germany;Department of Mathematics, University of Illinois, Urbana, IL 61801, USA
Venue:
Journal of Combinatorial Theory Series B
Year:
2012

Citing 6
Cited 0

A cycle structure theorem for Hamiltonian graphs

Journal of Combinatorial Theory Series A
Hamiltonian degree conditions which imply a graph is pancyclic

Journal of Combinatorial Theory Series B
The number of cycle lengths in graphs of given minimum degree and girth

Discrete Mathematics
Weakly pancyclic graphs

Journal of Combinatorial Theory Series B
Cycle lengths in sparse graphs

Combinatorica
Cycle Lengths in Hamiltonian Graphs with a Pair of Vertices Having Large Degree Sum

Graphs and Combinatorics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We prove that every Hamiltonian graph with n vertices and m edges has cycles with more than p-12lnp-1 different lengths, where p=m-n. For general m and n, there exist such graphs having at most 2@?p+1@? different cycle lengths.