On the complexity of recognizing tough graphs
β Scribed by Douglas Bauer; Aurora Morgana; Edward Schmeichel
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 252 KB
- Volume
- 124
- Category
- Article
- ISSN
- 0012-365X
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## Abstract Let hom (__G, H__) be the number of homomorphisms from a graph __G__ to a graph __H__. A wellβknown result of LovΓ‘sz states that the function hom (Β·, __H__) from all graphs uniquely determines the graph __H__ up to isomorphism. We study this function restricted to smaller classes of gra
Let G be a graph and let t Υ 0 be a real number. Then, We discuss how the toughness of (spanning) subgraphs of G and related graphs depends on (G), we give some sufficient degree conditions implying that (G) Υ t, and we study which subdivisions of 2-connected graphs have minimally 2-tough squares.
It is shown that the shortness exponent of the class of l-tough, maximal planar graphs is at most log, 5. The non-Hamiltonian, l-tough, maximal planar graph with a minimum number of vertices is presented.