A cycle in a graph is dominating if every vertex lies at distance at most one from the cycle and a cycle is D-cycle if every edge is incident with a vertex of the cycle. In this paper, first we provide recursive formulae for finding a shortest dominating cycle in a Hahn graph; minor modifications ca
Finding minimum dominating cycles in permutation graphs
β Scribed by Charles J Colbourn; J.Mark Keil; Lorna K Stewart
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 412 KB
- Volume
- 4
- Category
- Article
- ISSN
- 0167-6377
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π SIMILAR VOLUMES
Flandrin et ai. (to appear) define a simple bipartite graph to be biclaw-free if it contains no induced subgraph isomorphic to H, where H could be obtained from two copies of K1.3 by adding an edge joining the two vertices of degree 3. They have shown that if G is a bipartite, balanced, biclaw-free
Jackson, B., H. Li and Y. Zhu, Dominating cycles in regular 3-connected graphs, Discrete Mathematics 102 (1992) 163-176. Let G be a 3-connected, k-regular graph on at most 4k vertices. We show that, for k > 63, every longest cycle of G is a dominating cycle. We conjecture that G is in fact hamilton
Vu Dinh, H., On the length of longest dominating cycles in graphs, Discrete Mathematics 121 (1993) 21 l-222. ## A cycle C in an undirected and simple graph if G contains a dominating cycle. There exists l-tough graph in which no longest cycle is dominating. Moreover, the difference of the length