We describe a new type of sufficient condition for a digraph to be Hamiltonian. Conditions of this type combine local structure of the digraph with conditions on the degrees of nonadjacent vertices. The main difference from earlier conditions is that we do not require a degree condition on all pairs
A sufficient condition for a digraph to be kernel-perfect
β Scribed by P. Duchet
- Publisher
- John Wiley and Sons
- Year
- 1987
- Tongue
- English
- Weight
- 205 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The total chromatic number Ο T (G) of graph G is the least number of colors assigned to V (G) βͺ E(G) such that no adjacent or incident elements receive the same color. In this article, we give a sufficient condition for a bipartite graph G to have Ο T (G) = β(G) + 1.
## Abstract A proper vertex coloring of a graph __G__ = (__V, E__) is acyclic if __G__ contains no bicolored cycle. Given a list assignment __L__ = {__L__(__v__)|__v__β__V__} of __G__, we say __G__ is acyclically __L__βlist colorable if there exists a proper acyclic coloring Ο of __G__ such that Ο(
## Abstract Restricted edge connectivity is a more refined network reliability index than edge connectivity. A restricted edge cut __F__ of a connected graph __G__ is an edge cut such that __G__β__F__ has no isolated vertex. The restricted edge connectivity Ξ»β² is the minimum cardinality over all re
We introduce new necessary conditions, k-quasi-hamiltonicity (0 k n&1), for a digraph of order n to be hamiltonian. Every (k+1)-quasi-hamiltonian digraph is also k-quasi-hamiltonian; we construct digraphs which are k-quasi-hamiltonian, but not (k+1)-quasi-hamiltonian. We design an algorithm that che