Regular subgraphs of dense graphs
β Scribed by L. Pyber
- Book ID
- 110564298
- Publisher
- Springer-Verlag
- Year
- 1985
- Tongue
- English
- Weight
- 100 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0209-9683
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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