On covers of graphs
✍ Scribed by Maxová Jaroslav; Jana Nešetřil
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 171 KB
- Volume
- 5
- Category
- Article
- ISSN
- 1571-0653
No coin nor oath required. For personal study only.
✦ Synopsis
We concentrate on two problems from the area of coverings of graphs, on an oriented version of Perfect Path Double Cover (PPDC) and on oriented version of Weighted Cycle Cover.
📜 SIMILAR VOLUMES
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.
Regular covers of complete graphs which are 2-arc-transitive are investigated. A classification is given of all such graphs whose group of covering transformations is either cyclic or isomorphic to Z p \_Z p , where p is a prime and whose fibrepreserving subgroup of automorphisms acts 2-arc-transiti
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.