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 a Lemma of Gromov and the Entropy of a Graph
β Scribed by Fabio Scarabotti
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 42 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
β¦ Synopsis
If G is a finite, directed, simple and irreducible graph, deletion of an edge makes the entropy decrease. We give a proof of this fact that avoids the Perron-Frobenius theorem and makes use of a technique developed by Gromov.
π SIMILAR VOLUMES
## Abstract The eulericity Ο΅(__G__) of a bridgeless graph __G__ is defined as the least number of eulerian subgraphs of __G__ which together cover the lines of __G__. A 1β1 correspondence is shown to exist between the __k__βtuples of eulerian subgraphs of __G__ and the proper flows (mod2^__k__^) on
Recently, Andrews and Berkovich introduced a trinomial version of Bailey's lemma. In this note we show that each ordinary Bailey pair gives rise to a trinomial Bailey pair. This largely widens the applicability of the trinomial Bailey lemma and proves some of the identities proposed by Andrews and B
## Abstract This paper presents some recent results on lower bounds for independence ratios of graphs of positive genus and shows that in a limiting sense these graphs have the same independence ratios as do planar graphs. This last result is obtained by an application of Menger's Theorem to show t