Nous montrons que dans la classe des graphes connexes tels ;lue deux a&es incidentes quelconques appartiennent a un et un seul quadrilatere, les hypercrtbes finis sont les graphes de degre minimum n lini et possedant 2" sommets. The fol!owing theorem' is proved: Let % be the class of connected grap
A characterization of hypercubes
β Scribed by S. Foldes
- Publisher
- Elsevier Science
- Year
- 1977
- Tongue
- English
- Weight
- 306 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
Burosch, G., I. Have1 and J.-M. Laborde, Distance monotone graphs and a new characterization of hypercubes, Discrete Mathematics 110 (1992) 9-16.
## Communicated by A. Tucker Abstract--Complemented graphs are a direct generalization of hypercubes as well as a special class of prime convex intersection graphs. The n-tuple representation of points of a hypercube Qn is extended to prime convex intersection graphs.
Spanning trees of the hypercube Q n have been recently studied by several authors. In this paper, we construct spanning trees of Q n which are caterpillars and establish quantitative bounds for a caterpillar to span Q n . As a corollary, we disprove a conjecture of Harary and Lewinter on the length