A p-intersection representation of a graph G is a map, f, that assigns each vertex a subset of [1, 2, ..., t] The symbol % p (G) denotes this minimum t such that a p-intersection representation of G exists. In 1966 Erdo s, Goodman, and Po sa showed that for all graphs G on 2n vertices, % 1 (G) % 1
Unbalanced Star-Factorizations of Complete Bipartite Graphs II
โ Scribed by Nigel Martin
- Publisher
- Springer Japan
- Year
- 2007
- Tongue
- English
- Weight
- 188 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We conclude the study of complete K1,q-factorizations of complete bipartite graphs of the form Kn,n and show that, so long as the obvious Basic Arithmetic Conditions are satisfied, such complete factorizations must exist.
Let ยต be an eigenvalue of the graph G with multiplicity m. A star complement for ยต in G is an induced subgraph G -X such that |X| = m and ยต is not an eigenvalue of G -X. Some general observations concerning graphs with the complete bipartite graph K r,s (r + s > 2) as a star complement are followed
P,-factorization of K,,,, is (i) m + n -0 (mod 3), (ii) m < 2n, (iii) n s 2m and (iv) 3mn/2(m + n) is an integer.