𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Number of labeled 4-regular graphs

✍ Scribed by R. C. Read; N. C. Wormald


Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
305 KB
Volume
4
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis


Abstract

Several operations on 4‐regular graphs and pseudographs are analyzed and equations are obtained relating the numbers of these graphs on given numbers of labeled points. These equations are used recursively to find the numbers of 4‐regular graphs on up to 13 labeled points.


📜 SIMILAR VOLUMES


Regular graphs with prescribed chromatic
✍ L. Caccetta; N. J. Pullman 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 200 KB

## Abstract We determine the minimum number of edges in a regular connected graph on __n__ vertices, containing a complete subgraph of order __k__ ≤ __n__/2. This enables us to confirm and strengthen a conjecture of P. Erdös on the existence of regular graphs with prescribed chromatic number.

Regular factors of regular graphs
✍ B. Bollobás; Akira Saito; N. C. Wormald 📂 Article 📅 1985 🏛 John Wiley and Sons 🌐 English ⚖ 242 KB

Given r 3 3 and 1 s A s r, we determine all values of k for which every r-regular graph with edge-connectivity A has a k-factor. Some of the earliest results in graph theory are due to Petersen [8] and concern factors in graphs. Among others, Petersen proved that a regular graph of even degree has a

P4-decompositions of regular graphs
✍ Heinrich, Katherine; Liu, Jiping; Yu, Minli 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 246 KB 👁 1 views

In this article, we show that every simple r-regular graph G admits a balanced P 4 -decomposition if r ≡ 0(mod 3) and G has no cut-edge when r is odd. We also show that a connected 4-regular graph G admits a P 4 -decomposition if and only if |E(G)| ≡ 0(mod 3) by characterizing graphs of maximum degr

Compatible circuit decompositions of 4-r
✍ Herbert Fleischner; François Genest; Bill Jackson 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 210 KB

## Abstract A transition system __T__ of an Eulerian graph __G__ is a family of partitions of the edges incident to each vertex of __G__ into transitions, that is, subsets of size two. A circuit decomposition $\cal C$ of __G__ is compatible with __T__ if no pair of adjacent edges of __G__ is both a

3-colorability of 4-regular hamiltonian
✍ Herbert Fleischner; Gert Sabidussi 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 187 KB 👁 1 views

## Abstract On the model of the cycle‐plus‐triangles theorem, we consider the problem of 3‐colorability of those 4‐regular hamiltonian graphs for which the components of the edge‐complement of a given hamiltonian cycle are non‐selfcrossing cycles of constant length ≥ 4. We show that this problem is