Quotients of connected regular graphs of even degree
✍ Scribed by Jozef Širáň; Martin Škoviera
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 669 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract In 1960, Dirac posed the conjecture that __r__‐connected 4‐critical graphs exist for every __r__ ≥ 3. In 1989, Erdős conjectured that for every __r__ ≥ 3 there exist __r__‐regular 4‐critical graphs. In this paper, a technique of constructing __r__‐regular __r__‐connected vertex‐transiti
Let G be a k-regular 2-connected graph of order n. Jackson proved that G is hamiltonian if n 5 3k. Zhu and Li showed that the upper bound 3k on n can be relaxed to q k if G is 3-connected and k 2 63. We improve both results by showing that G is hamiltonian if n 5 gk -7 and G does not belong to a res
Let 1 denote a bipartite Q-polynomial distance-regular graph with diameter D 4. We show that 1 is the quotient of an antipodal distance-regular graph if and only if one of the following holds. (i) 1 is a cycle of even length. (ii) 1 is the quotient of the 2D-cube. 1999 Academic Press \* , ..., %\
A p-factor of a graph G is a regular spanning subgraph of degree p . For G regular of degree d ( G ) and order 2n, let ( p l , ..., p,) be a partition of d ( G ) , so that p i > 0 ( I S i S r ) and p , i i pr = d(G). If H I . ..., H, are edge-disjoint regular spanning subgraphs of G of degrees p I ,
## Abstract By Petersen's theorem, a bridgeless cubic graph has a 2‐factor. H. Fleischner extended this result to bridgeless graphs of minimum degree at least three by showing that every such graph has a spanning even subgraph. Our main result is that, under the stronger hypothesis of 3‐edge‐connec