✦ LIBER ✦

Long cycles, degree sums and neighborhood unions

✍ Scribed by H.J. Broersma; J.van den Heuvel; H.J. Veldman

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 747 KB
Volume: 121
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90534-z

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

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.

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

Long dominating cycles and paths in grap

Long dominating cycles and paths in graphs with large neighborhood unions

✍ H. J. Broersma; H. J. Veldman 📂 Article 📅 1991 🏛 John Wiley and Sons 🌐 English ⚖ 413 KB 👁 1 views

## Abstract Let __G__ be a graph of order __n__ and define __NC(G)__ = min{|__N__(__u__) ∪ __N__(__v__)| |__uv__ ∉ __E__(__G__)}. A cycle __C__ of __G__ is called a __dominating cycle__ or __D__‐__cycle__ if __V__(__G__) ‐ __V__(__C__) is an independent set. A __D__‐__path__ is defined analogously.

Long cycles in graphs with large degree

Long cycles in graphs with large degree sums

✍ Douglas Bauer; H.J. Veldman; A. Morgana; E.F. Schmeichel 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 764 KB

Degree Sums and Covering Cycles

✍ Hikoe Enomoto; Atsushi Kaneko; Mekkia Kouider; Zsolt Tuza 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 194 KB

## Abstract It is shown that if in a simple graph __G__ of order __n__ the sum of degrees of any three pairwise non‐adjacent vertices is at least __n__, then there are two cycles (or one cycle and an edge or a vertex) of __GF__ that contain all the vertices. © 1995 John Wiley & Sons, Inc.

Hamiltonism, degree sum and neighborhood

Hamiltonism, degree sum and neighborhood intersections

✍ E. Flandrin; H.A. Jung; H. Li 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 715 KB

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.