Partitions of digraphs into paths or circuits
β Scribed by W. Bienia; H. Meyniel
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 178 KB
- Volume
- 61
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
The problem of partitioning the arcs of a digraph into elementary paths has been considered first by B. Alspach and N.J. Pullman in . We consider the slightly different problem of partitioning the arcs of a digraph into elementary paths or circuits. A general conjecture is given which is solved in particular cases (with in fact slightly stronger results).
π SIMILAR VOLUMES
For a graph G, let ' 2 (G ) denote the minimum degree sum of a pair of nonadjacent vertices. We conjecture that if |V(G)| n i 1 k a i and ' 2 (G ) ! n k Γ 1, then for any k vertices v 1 , v 2 , F F F , v k in G, there exist vertex-disjoint paths P 1 , P 2 , F F F , P k such that |V (P i )| a i and v
It is shown in this note that it can be recognized in polynomial time whether the vertex set of a finite undirected graph can be partitioned into one or two independent sets and one or two cliques. Such graphs generalize bipartite and split graphs and the result also shows that it can be recognized