## Abstract Let __G__ be a finite graph with directed bipartition (__V__^+^, __V__^โ^). Necessary and sufficient conditions are given for the existence of covers and strong covers that: (i) satisfy matching with respect to __V__^+^, and (ii) include a given set of edges that satisfies matching with
Covers of graphs and EGQs
โ Scribed by Peter J. Cameron
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 645 KB
- Volume
- 97
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
The puposes of this paper is the construction of some new extended generalized quadrangles, as covers of known esamples. The construction requires the vanishing of cohomology of certain simplicial complexes. One of the constructions generalizes to give some distance-regular antipodal covers of complete graphs, some of which also appear to be new.
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.
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.
Let (G, w ) denote a simple graph G with a weight function w : โฌ(G) -{0,1,2}. A path cover of (G, w ) is a collection of paths in G such that every edge e is contained in exactly w(e) paths of the collection. For a vertex u , w ( v ) is the sum of the weights of the edges incident with U ; U is call