## Abstract There are many results concerned with the hamiltonicity of __K__~1,3~‐free graphs. In the paper we show that one of the sufficient conditions for the __K__~1,3~‐free graph to be Hamiltonian can be improved using the concept of second‐type vertex neighborhood. The paper is concluded with
Pairs of Hamiltonian circuits in 5-connected planar graphs
✍ Scribed by Joseph Zaks
- Publisher
- Elsevier Science
- Year
- 1976
- Tongue
- English
- Weight
- 763 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0095-8956
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## Abstract It is shown that every sufficiently large almost‐5‐connected non‐planar graph contains a minor isomorphic to an arbitrarily large graph from one of six families of graphs. The graphs in these families are also almost‐5‐connected, by which we mean that they are 4‐connected and all 4‐sepa
A graph is said to be projective-planar if it is nonplanar and is embeddable in a projective plane. In this paper we show that the numbers of projectiveplanar embeddings (up to equivalence) of all 5-connected graphs have an upper bound c( 1120).
a b s t r a c t Assume that n and δ are positive integers with 3 ≤ δ < n. Let hc(n, δ) be the minimum number of edges required to guarantee an n-vertex graph G with minimum degree δ(G) ≥ δ to be hamiltonian connected.