4-Regular Graphs without 3-Regular Subgraphs
β Scribed by LIMIN ZHANG
- Book ID
- 119862816
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 457 KB
- Volume
- 576
- Category
- Article
- ISSN
- 0890-6564
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## Abstract Berge conjectured that every finite simple 4βregular graph __G__ contains a 3βregular subgraph. We prove that this conjecture is true if the cyclic edge connectivity Ξ»^__c__^(__G__) of __G__ is at least 10. Also we prove that if __G__ is a smallest counterexample, then Ξ»^__c__^(__G__) i
For any 4-regular graph G (possibly with multiple edges), we prove that, if the number N of distinct Euler orientations of G is such that N β‘ 1 (mod 3), then G has a 3-regular subgraph. It gives the new 4-regular graphs with multiple edges which have no 3-regular subgraphs, for which we know the num