✦ LIBER ✦

Hamiltonism, degree sum and neighborhood intersections

✍ Scribed by E. Flandrin; H.A. Jung; H. Li

Publisher: Elsevier Science
Year: 1991
Tongue: English
Weight: 715 KB
Volume: 90
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90094-i

No coin nor oath required. For personal study only.

✦ Synopsis

We give a sufficient condition for hamiltonism of a 2-connected graph involving the degree sum and the neighborhood intersection of any three independent vertices.

📜 SIMILAR VOLUMES

Insertible vertices, neighborhood inters

Insertible vertices, neighborhood intersections, and hamiltonicity

✍ A. Ainouche; I. Schiermeyer 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 475 KB

## Abstract Let __G__ be a simple undirected graph of order __n__. For an independent set __S__ ⊂ __V__(__G__) of __k__ vertices, we define the __k__ neighborhood intersections __S__~__i__~ = {__v__ ϵ __V__(__G__)\__S__|__N__(__v__) ∩ S| = __i__}, 1 ≦ __i__ ≦ __k__, with __s__~__i__~ = |__S__~__i__

Long cycles, degree sums and neighborhoo

Long cycles, degree sums and neighborhood unions

✍ H.J. Broersma; J.van den Heuvel; H.J. Veldman 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 747 KB

Long cycles in graphs with large degree

Long cycles in graphs with large degree sums and neighborhood unions

✍ Van den Heuvel, J. 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 801 KB

We present and prove several results concerning the length of longest cycles in 2connected or I-tough graphs with large degree sums. These results improve many known results on long cycles in these graphs. We also consider the sharpness of the results and discuss some possible strengthenings.

Hamiltonian graphs with neighborhood int

Hamiltonian graphs with neighborhood intersections

✍ G. Chen; R. H. Schelp 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 577 KB

## Abstract In this paper, __k__ + 1 real numbers __c__~1~, __c__~2~, ⃛, __c__~__k__+1~ are found such that the following condition is sufficient for a __k__‐connected graph of order __n__ to be hamiltonian: for each independent vertex set of __k__ + 1 vertices in __G__. magnified image where S~i~

Neighborhood unions and hamilton cycles

✍ Bill Jackson 📂 Article 📅 1991 🏛 John Wiley and Sons 🌐 English ⚖ 392 KB

## Abstract Let __G__ be a graph on __n__ vertices and __N__~2~(__G__) denote the minimum size of __N__(__u__) ∪ __N__(__v__) taken over all pairs of independent vertices __u, v__ of __G__. We show that if __G__ is 3‐connected and __N__~2~(__G__) ⩾ ½(__n__ + 1), then __G__ has a Hamilton cycle. We

Neighborhood unions and hamiltonicity of

Neighborhood unions and hamiltonicity of graphs

✍ Ruqun Shen; Feng Tian 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 530 KB

Let G be a graph of order n. In this paper, we prove that if G is a 2-connected graph of order n such that for all u, ve V(G), 2 where dist(u,v) is the distance between u and v in G, then either G is hamiltonian, or G is a spanning subgraph of a graph in one of three families of exceptional graphs.