✦ LIBER ✦

Maximal cycles in graphs

✍ Scribed by L. Caccetta; K. Vijayan

Publisher: Elsevier Science
Year: 1991
Tongue: English
Weight: 395 KB
Volume: 98
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90407-s

No coin nor oath required. For personal study only.

✦ Synopsis

Caccetta, L. and K. Vijayan, Maximal cycles in graphs, Discrete Mathematics 98 (1991) l-7.

Let G be a simple graph on n vertices and m edges having circumference (longest cycle length) 1. Woodall determined some time ago the maximum possible value of m. The object of this paper is to give an alternative proof of Woodall's theorem. Our approach will, in addition, characterize the structure of the extremal graphs.

📜 SIMILAR VOLUMES

Maximal sets of hamilton cycles in compl

Maximal sets of hamilton cycles in complete multipartite graphs

✍ Mike Daven; J. A. MacDougall; C. A. Rodger 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 154 KB 👁 2 views

## Abstract A set __S__ of edge‐disjoint hamilton cycles in a graph __G__ is said to be __maximal__ if the edges in the hamilton cycles in __S__ induce a subgraph __H__ of __G__ such that __G__ − __E__(__H__) contains no hamilton cycles. In this context, the spectrum __S__(__G__) of a graph __G__ i

Uniqueness of maximal dominating cycles

Uniqueness of maximal dominating cycles in 3-regular graphs and of hamiltonian cycles in 4-regular graphs

✍ Herbert Fleischner 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 461 KB 👁 2 views

## Abstract We construct 3‐regular (cubic) graphs __G__ that have a dominating cycle __C__ such that no other cycle __C__~1~ of __G__ satisfies __V(C)__ ⊆ __V__(__C__~1~). By a similar construction we obtain loopless 4‐regular graphs having precisely one hamiltonian cycle. The basis for these const

Maximal independent sets in graphs with

Maximal independent sets in graphs with at most r cycles

✍ Goh Chee Ying; Koh Khee Meng; Bruce E. Sagan; Vincent R. Vatter 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 127 KB 👁 2 views

## Abstract We find the maximum number of maximal independent sets in two families of graphs. The first family consists of all graphs with __n__ vertices and at most __r__ cycles. The second family is all graphs of the first family which are connected and satisfy __n__ ≥ 3__r__. © 2006 Wiley Period

Maximal and maximum independent sets in

Maximal and maximum independent sets in graphs with at most r cycles

✍ Bruce E. Sagan; Vincent R. Vatter 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 236 KB 👁 2 views

## Abstract Let __m__(__G__) denote the number of maximal independent sets of vertices in a graph __G__ and let __c__(__n__,__r__) be the maximum value of __m__(__G__) over all connected graphs with __n__ vertices and at most __r__ cycles. A theorem of Griggs, Grinstead, and Guichard gives a formul

Maximality of the cycle code of a graph

✍ Patrick Solé; Thomas Zaslavsky 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 274 KB

The cycle code of a graph is the binary linear span of the characteristic vectors of circuits. We characterize the graphs whose cycle codes are maximal for the packing problem, based on characterizing the graphs whose girth is at least :(n-c)+ 1 where n and c are the numbers of vertices and connecte

On the number of hamiltonian cycles in a

On the number of hamiltonian cycles in a maximal planar graph

✍ S. L. Hakimi; E. F. Schmeichel; C. Thomassen 📂 Article 📅 1979 🏛 John Wiley and Sons 🌐 English ⚖ 243 KB 👁 2 views

## Abstract We consider the problem of the minimum number of Hamiltonian cycles that could be present in a Hamiltonian maximal planar graph on __p__ vertices. In particular, we construct a __p__‐vertex maximal planar graph containing exactly four Hamiltonian cycles for every __p__ ≥ 12. We also pro