Cited By
View all- Fleischner HHäggkvist R(2018)Cycle Double Covers in Cubic Graphs having Special StructuresJournal of Graph Theory10.1002/jgt.2177977:2(158-170)Online publication date: 31-Dec-2018
A Note on 5-Cycle Double Covers
Pages 977 - 979
Abstract
The strong cycle double cover conjecture states that for every circuit C of a bridgeless cubic graph G, there is a cycle double cover of G which contains C. We conjecture that there is even a 5-cycle double cover S of G which contains C, i.e. C is a subgraph of one of the five 2-regular subgraphs of S. We prove a necessary and sufficient condition for a 2-regular subgraph to be contained in a 5-cycle double cover of G.
References
[1]
Bondy J.A., Murty U.S.R.: Graph Theory. Springer, Berlin (2008)
[2]
Brinkmann, G., Goedgebeur, J., Hägglund, J., Markström, K.: Generation and Properties of Snarks. Manuscript
[3]
Celmins, U.A.: On cubic graphs that do not have an edge-3-coloring. Ph.D. Thesis, University of Waterloo (1984)
[4]
Goddyn, L.: Cycle covers of graphs. Ph.D. Thesis, University of Waterloo (1984)
[5]
Huck A., Kochol M.: Five cycle double covers of some cubic graphs. J. Combin. Theory Ser. B 64(1), 119---125 (1995)
[6]
Preissmann M.: Sur les coloration des arets des graphs cubiques. These de Doctorat, Grenoble (1981)
[7]
Zhang C.Q.: Integer Flows and Cycle Covers of Graphs. Marcel Dekker, New York (1997)
Index Terms
- A Note on 5-Cycle Double Covers
Index terms have been assigned to the content through auto-classification.
Recommendations
Cycle double covers and spanning minors I
Define a graph to be a Kotzig graph if it is m-regular and has an m-edge colouring in which each pair of colours form a Hamiltonian cycle. We show that every cubic graph with spanning subgraph consisting of a subdivision of a Kotzig graph together with ...
Flows, flow-pair covers and cycle double covers
In this paper, some earlier results by Fleischner [H. Fleischner, Bipartizing matchings and Sabidussi's compatibility conjecture, Discrete Math. 244 (2002) 77-82] about edge-disjoint bipartizing matchings of a cubic graph with a dominating circuit are ...
Contractions, cycle double covers, and cyclic colorings in locally connected graphs
A finite, undirected graph is called locally connected, if the neighborhood of every vertex induces a connected subgraph. In this paper we study the existence of edges in locally connected k-connected graphs whose contraction keeps the graph locally ...
Comments
Information & Contributors
Information
Published In
Copyright © Copyright © 2013 Springer Japan.
Publisher
Springer-Verlag
Berlin, Heidelberg
Publication History
Published: 01 July 2013
Author Tag
Qualifiers
- Article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- View Citations1Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 30 Aug 2024
Other Metrics
Citations
Cited By
View all- Fleischner HHäggkvist R(2018)Cycle Double Covers in Cubic Graphs having Special StructuresJournal of Graph Theory10.1002/jgt.2177977:2(158-170)Online publication date: 31-Dec-2018
View Options
View options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in