Given a graph G, its odd set is a set of all integers k such that G has odd number of vertices of degree k. We show that if two graphs G and H of the same order have the same odd sets then they can be obtained from each other by succesive application of the following two operations: โข add or remove
Graphs with Odd Cocliques
โ Scribed by Brouwer, A.E.; Shult, E.E.
- Book ID
- 123003513
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 425 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Gyarf&, A., Graphs with k odd cycle lengths, Discrete Mathematics 103 (1992) 41-48. If G is a graph with k z 1 odd cycle lengths then each block of G is either KZk+2 or contains a vertex of degree at most 2k. As a consequence, the chromatic number of G is at most 2k + 2. For a graph G let L(G) deno
The purpose of this note is to present a polynomial-time algorithm which, given an arbitrary graph G as its input, finds either a proper 3-coloring of G or an odd-K4 that is a subgraph of G in time O(mn), where m and n stand for the number of edges and the number of vertices of G, respectively. (~