Let i be a positive integer. We generalize the chromatic number x ( G ) of G and the clique number w(G) of G as follows: The i-chromatic number of G , denoted by x Z ( G ) , is the least number k for which G has a vertex partition V,, V,, . . . , Vk: such that the clique number of the subgraph induc
A family of perfect graphs associated with directed graphs
โ Scribed by Jeff Kahn
- Publisher
- Elsevier Science
- Year
- 1984
- Tongue
- English
- Weight
- 189 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The Strong Perfect Graph Conjecture states that a graph is perfect iff neither it nor its complement contains an odd chordless cycle of size greater than or equal to 5. In this article it is shown that many families of graphs are complete for this conjecture in the sense that the conjecture is true
A 1-factorisation of a graph is perfect if the union of any two of its 1-factors is a Hamiltonian cycle. Let n=p 2 for an odd prime p. We construct a family of ( p -1)/2 non-isomorphic perfect 1-factorisations of K n, n . Equivalently, we construct pan-Hamiltonian Latin squares of order n. A Latin s
Let S be an arbitrary collection of stars in a graph G such that there is no chain of length ~3 joining the centers of (any) two stars in G. We consider the graphs that can be obtained by deleting in a parity graph all the edges of such a set S. These graphs will be called skeletal graphs and we pro