On cycle double covers of line graphs
โ Scribed by Leizhen Cai; Derek Corneil
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 257 KB
- Volume
- 102
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
It is shown that if a graph has a cycle double cover, then its line graph also has a cycle double cover. The converse of this result for 2-edge-connected graphs would imply the truth of the cycle double cover conjecture.
Cycle Double Cover Conjecture (CDCC). Every 2-edge-connected graph has a CDC.
๐ SIMILAR VOLUMES
Some new results on minimum cycle covers are proved. As a consequence, it is obtained that the edges of a bridgeless graph G can be covered by cycles of total length at most |E(G)| + 25 24 (|V (G)| -1), and at most |E(G)| + |V (G)| -1 if G contains no circuit of length 8 or 12.
## Seyffarth, K., Hajos' conjecture and small cycle double covers of planar graphs, Discrete Mathematics 101 (1992) 291-306. We prove that every simple even planar graph on n vertices has a partition of its edge set into at most [(n -1)/2] cycles. A previous proof of this result was given by Tao,
Let O(G) denote the set of odd-degree vertices of a graph G. Let t E N and let 9, denote the family of graphs G whose edge set has a partition This partition is associated with a double cycle cover of G. We show that if a graph G is at most 5 edges short of being 4-edge-connected, then exactly one
Any group of automorphisms of a graph G induces a notion of isomorphism between double covers of G. The corresponding isomorphism classes will be counted.
## Abstract Let __G__ be a bridgeless cubic graph. We prove that the edges of __G__ can be covered by circuits whose total length is at most (44/27) |__E(G)__|, and if Tutte's 3โflow Conjecture is true, at most (92/57) |__E(G)__|.