## 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.
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.
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