Hostname: page-component-77f85d65b8-5ngxj Total loading time: 0 Render date: 2026-03-30T09:50:27.956Z Has data issue: false hasContentIssue false
  • English
  • Français

(1, 2)-Factorizations of General Eulerian Nearly Regular Graphs

Published online by Cambridge University Press:  12 September 2008

Roland Häggkvist  and
Anders Johansson
Roland Häggkvist
Affiliation:
Department of Mathematics, University of Umeå, S-901 87 Umeå, SwedenE-mail address:rolandh@biovax.umdc.umu.se, andersj@zeus.cs.umu.se
Anders Johansson
Affiliation:
Department of Mathematics, University of Umeå, S-901 87 Umeå, SwedenE-mail address:rolandh@biovax.umdc.umu.se, andersj@zeus.cs.umu.se
Get access Rights & Permissions [Opens in a new window]

Abstract

Every general graph with degrees 2k and 2k − 2, k ≥ 3, with zero or at least two vertices of degree 2k − 2 in each component, has a k-edge-colouring such that each monochromatic subgraph has degree 1 or 2 at every vertex.

In particular, if T is a triangle in a 6-regular general graph, there exists a 2-factorization of G such that each factor uses an edge in T if and only if T is non-separating.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 1 , March 1994 , pp. 87 - 95
Copyright
Copyright © Cambridge University Press 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1]Andersen, L. D. et al. (1992) Special volume to mark the centennial of Julius Petersen's ‘Die Theorie der regulären Graphs’. Discrete Mathematics 100 101.Google Scholar
[2]Häggkvist, R. (1976) A solution of the Evans conjecture for Latin squares of large size. In: Proceedings Fifth Hungarian Colloquium, Keszthely 1976, vol. 1. Combinatorics 18.Google Scholar
[3]Hilton, A. J. W. and Rodger, C. A. (1991) Edge-colouring regular bipartite graphs. Graph theory (Cambridge, 1981) 56. North-Holland, Amsterdam-New York, 139–158.Google Scholar
[4]Hilton, A. J. W. and Rodger, C. A. (1990) Edge-Colouring Graphs and Embedding Partial Triple Systems of Even Index. Cycles and Rays (NATO ASI Series, eds.), Kluwer, 101–112.CrossRefGoogle Scholar
[5]Hilton, A. J. W. and Rodger, C. A. (1991) The Embedding of Partial Triple Systems when 4 Divides lambda. Journal of Combinatorial Theory Series A 56 109–137.CrossRefGoogle Scholar
[6]Johansson, A. (1993) A Note on Embedding Partial Triple Systems of Even Index (in preparation).Google Scholar
[7]Petersen, J. (1891) Die Theorie der regulären Graphs. Acta Mathematica 15 193–220.CrossRefGoogle Scholar
[8]Sabidussi, G. (1993) Parity Equivalence in Eulerian Graphs (preprint).Google Scholar