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
The Cycle Discrepancy of Three-Regular Graphs
β Scribed by Sarmad Abbasi; Laeeq Aslam
- Book ID
- 106047900
- Publisher
- Springer Japan
- Year
- 2010
- Tongue
- English
- Weight
- 400 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
## 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
## Abstract We construct 3βregular (cubic) graphs __G__ that have a dominating cycle __C__ such that no other cycle __C__~1~ of __G__ satisfies __V(C)__ β __V__(__C__~1~). By a similar construction we obtain loopless 4βregular graphs having precisely one hamiltonian cycle. The basis for these const