𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On shortest cocycle covers of graphs

✍ Scribed by François Jaeger; Abdelkader Khelladi; Michel Mollard


Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
738 KB
Volume
39
Category
Article
ISSN
0095-8956

No coin nor oath required. For personal study only.


📜 SIMILAR VOLUMES


Shortest Circuit Covers of Cubic Graphs
✍ B. Jackson 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 298 KB

We show that the edge set of a bridgeless cubic graph \(G\) can be covered with circuits such that the sum of the lengths of the circuits is at most \(\frac{64}{39}|E(G)|\). Stronger results are obtained for cubic graphs of large girth. 1994 Academic Press, Inc.

A note on shortest cycle covers of cubic
✍ Xinmin Hou; Cun-Quan Zhang 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 92 KB 👁 1 views

## Abstract Let __SCC__~3~(__G__) be the length of a shortest 3‐cycle cover of a bridgeless cubic graph __G__. It is proved in this note that if __G__ contains no circuit of length 5 (an improvement of Jackson's (__JCTB 1994__) result: if __G__ has girth at least 7) and if all 5‐circuits of __G_

Cycle and cocycle coverings of graphs
✍ Sean McGuinness 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 161 KB

In this article, we show that for any simple, bridgeless graph G on n vertices, there is a family C of at most n-1 cycles which cover the edges of G at least twice. A similar, dual result is also proven for cocycles namely: for any loopless graph G on n vertices and edges having cogirth g \* ≥ 3 and

Cycle-cocycle partitions and faithful cy
✍ Henning Bruhn; Reinhard Diestel; Maya Stein 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 112 KB

## Abstract By a result of Gallai, every finite graph __G__ has a vertex partition into two parts each inducing an element of its cycle space. This fails for infinite graphs if, as usual, the cycle space is defined as the span of the edge sets of finite cycles in __G__. However, we show that, for t

On covers of graphs
✍ Maxová Jaroslav; Jana Nešetřil 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 171 KB

We concentrate on two problems from the area of coverings of graphs, on an oriented version of Perfect Path Double Cover (PPDC) and on oriented version of Weighted Cycle Cover.

On total covers of graphs
✍ Yousef Alavi; Jiuqiang Liu; Jianfang Wang; Zhongfu Zhang 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 292 KB