Mader proved that every 2-connected simple graph G with minimum degree d exceeding three has a cycle C, the deletion of whose edges leaves a 2-connected graph. Jackson extended this by showing that C may be chosen to avoid any nominated edge of G and to have length at least d-1. This article proves
Transversals of circuits and acyclic orientations in graphs and matroids
โ Scribed by C. Berge; M. Las Vergnas
- Publisher
- Elsevier Science
- Year
- 1984
- Tongue
- English
- Weight
- 132 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0012-365X
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The oriented chromatic number ฯ o ( G) of an oriented graph G = (V, A) is the minimum number of vertices in an oriented graph H for which there exists a homomorphism of G to H. The oriented chromatic number ฯ o (G) of an undirected graph G is the maximum of the oriented chromatic numbers of all the
## Abstract Given a digraph __D__ on vertices __v__~1~, __v__~2~, โ, __v__~__n__~, we can associate a bipartite graph __B(D)__ on vertices __s__~1~, __s__~2~, โ, __s__~__n__~, __t__~1~, __t__~2~, โ, __t__~__n__~, where __s__~__i__~__t__~__j__~ is an edge of __B(D)__ if (__v__~__i__~, __v__~__j__~)