✦ LIBER ✦

Face Size and the Maximum Genus of a Graph 1. Simple Graphs

✍ Scribed by Yuanqiu Huang; Yanpei Liu

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 150 KB
Volume: 80
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.2000.1990

No coin nor oath required. For personal study only.

✦ Synopsis

This paper shows that a simple graph which can be cellularly embedded on some closed surface in such a way that the size of each face does not exceed 7 is upper embeddable. This settles one of two conjectures posed by Nedela and S8 koviera (1990, in ``Topics in Combinatorics and Graph Theory,'' pp. 519 529, Physica Verlag, Heidelberg). The other conjecture will be proved in a sequel to this paper.

📜 SIMILAR VOLUMES

The Relative Maximum Genus of a Graph

✍ C.P. Bonnington 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 422 KB

Cochromatic Number and the Genus of a Gr

Cochromatic Number and the Genus of a Graph

✍ H. Joseph Straight 📂 Article 📅 1979 🏛 John Wiley and Sons 🌐 English ⚖ 310 KB 👁 1 views

## Abstract The cochromatic number of a graph __G__, denoted by __z__(__G__), is the minimum number of subsets into which the vertex set of __G__ can be partitioned so that each sbuset induces an empty or a complete subgraph of __G__. In this paper we introduce the problem of determining for a surf

A linear vizing-like relation between th

A linear vizing-like relation between the size and the domination number of a graph

✍ Rautenbach, Dieter 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 174 KB 👁 2 views

We prove m ≤ ∆n -(∆ + 1)γ for every graph without isolated vertices of order n, size m, domination number γ and maximum degree ∆ ≥ 3. This generalizes a result of Fisher et al., CU-Denver Tech Rep, 1996] who obtained the given bound for the case ∆ = 3.

A linear Vizing-like relation relating t

A linear Vizing-like relation relating the size and total domination number of a graph

✍ Michael A. Henning 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 77 KB

## Abstract We prove that __m__ ≤ Δ (__n__ − γ~t~) for every graph each component of which has order at least 3 of order __n__, size __m__, total domination number γ~t~, and maximum degree Δ ≥ 3. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 285–290, 2005

On the number of (r,r+1)- factors in an

On the number of (r,r+1)- factors in an (r,r+1)-factorization of a simple graph

✍ A. J. W. Hilton 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 113 KB 👁 1 views

## Abstract For integers __d__≥0, __s__≥0, a (__d, d__+__s__)‐__graph__ is a graph in which the degrees of all the vertices lie in the set {__d, d__+1, …, __d__+__s__}. For an integer __r__≥0, an (__r, r__+1)‐__factor__ of a graph __G__ is a spanning (__r, r__+1)‐subgraph of __G__. An (__r, r__+1)‐

Erratum to: “A linear vizing-like relati

Erratum to: “A linear vizing-like relation relating the size and total domination number of a graph”

✍ Erfang Shan; Liying Kang; Michael A. Henning 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 83 KB

## Abstract The proof of the main theorem in the paper [1] is incorrect as it is missing an important case. Here we complete the proof by giving the missing case. © 2007 Wiley Periodicals, Inc. J Graph Theory 54: 350–353, 2007