The hamiltonian path graph H(F) of a graph F is that graph having the same vertex set as F and in which two vertices u and u are adjacent if and only if F contains a hamiltonian u -u path. First, in response to a conjecture of Chartrand, Kapoor and Nordhaus, a characterization of nonhamiltonian grap
On minimum degree in Hamiltonian path graphs
✍ Scribed by George R. T. Hendry
- Publisher
- John Wiley and Sons
- Year
- 1988
- Tongue
- English
- Weight
- 294 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract A subset __S__ of vertices of a graph __G__ is __k__‐dominating if every vertex not in __S__ has at least __k__ neighbors in __S__. The __k__‐domination number $\gamma\_k(G)$ is the minimum cardinality of a __k__‐dominating set of __G__. Different upper bounds on $\gamma\_{k}(G)$ are kn
We give a simple proof that the obvious necessary conditions for a graph to contain the k th power of a Hamiltonian path are sufficient for the class of interval graphs. The proof is based on showing that a greedy algorithm tests for the existence of Hamiltonian path powers in interval graphs. We wi
## Abstract This article deals with a study of novel classes of metamaterial inclusions based on space‐filling curves. The graph–theoretic Hamiltonian‐path (HP) concept is exploited to construct a fairly broad class of space‐filling curve geometries that include as special cases the well‐known Hilb
## Abstract We investigate the minimization problem of the minimum degree of minimal Ramsey graphs, initiated by Burr et al. We determine the corresponding graph parameter for numerous bipartite graphs, including bi‐regular bipartite graphs and forests. We also make initial progress for graphs of l