✦ LIBER ✦

Minimal Graphs with Crossing Number at Least k

✍ Scribed by R.B. Richter; C. Thomassen

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 277 KB
Volume: 58
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.1993.1038

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

On 3-regular graphs having crossing numb

On 3-regular graphs having crossing number at least 2

✍ Dan McQuillan; R. Bruce Richter 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 414 KB

## Abstract We give a planar proof of the fact that if __G__ is a 3‐regular graph minimal with respect to having crossing number at least 2, then the crossing number of __G__ is 2.

Cubic graphs with crossing number two

✍ Bruce Richter 📂 Article 📅 1988 🏛 John Wiley and Sons 🌐 English ⚖ 360 KB

On Line Graphs with Crossing Number 1

✍ V. R. Kulli; D. G. Akka; L. W. Beineke 📂 Article 📅 1979 🏛 John Wiley and Sons 🌐 English ⚖ 159 KB

## Abstract In this paper we deduce a necessary and sufficient condition for a line grah to have crossing number 1. In addition, we prove that the line graph of any nonplanar graph has crossing number greater than 2.

Saturated graphs with minimal number of

Saturated graphs with minimal number of edges

✍ L. Kászonyi; Zs. Tuza 📂 Article 📅 1986 🏛 John Wiley and Sons 🌐 English ⚖ 286 KB

Let F = {F,, . . .} be a given class of forbidden graphs. A graph G is called F-saturated if no F, E F is a subgraph of G but the addition of an arbitrary new edge gives a forbidden subgraph. In this paper the minimal number of edges in F-saturated graphs is examined. General estimations are given a

Group chromatic number of planar graphs

Group chromatic number of planar graphs of girth at least 4

✍ Hong-Jian Lai; Xiangwen Li 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 212 KB 👁 1 views

## Abstract Jeager et al. introduced a concept of group connectivity as a generalization of nowhere zero flows and its dual concept group coloring, and conjectured that every 5‐edge connected graph is Z~3~‐connected. For planar graphs, this is equivalent to that every planar graph with girth at lea

Infinite families of crossing-critical g

Infinite families of crossing-critical graphs with prescribed average degree and crossing number

✍ Drago Bokal 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 242 KB 👁 1 views

## Abstract Širáň constructed infinite families of __k__‐crossing‐critical graphs for every __k__⩾3 and Kochol constructed such families of simple graphs for every __k__⩾2. Richter and Thomassen argued that, for any given __k__⩾1 and __r__⩾6, there are only finitely many simple __k__‐crossing‐criti