In this paper it is shown that any rn-regular graph of order 2rn (rn 3 3), not isomorphic to K, , , , or of order 2rn + 1 (rn even, rn 3 4), is Hamiltonian connected, which extends a previous result of Nash-Williams. As a corollary, it is derived that any such graph contains at least rn Hamiltonian
A class of Hamiltonian regular graphs
✍ Scribed by Paul Erdös; Arthur M. Hobbs
- Publisher
- John Wiley and Sons
- Year
- 1978
- Tongue
- English
- Weight
- 317 KB
- Volume
- 2
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
In this paper, we show that n ⩾ 4 and if G is a 2‐connected graph with 2__n__ or 2__n__−1 vertices which is regular of degree n−2, then G is Hamiltonian if and only if G is not the Petersen graph.
📜 SIMILAR VOLUMES
## Abstract On the model of the cycle‐plus‐triangles theorem, we consider the problem of 3‐colorability of those 4‐regular hamiltonian graphs for which the components of the edge‐complement of a given hamiltonian cycle are non‐selfcrossing cycles of constant length ≥ 4. We show that this problem is
## Abstract We construct 3‐regular (cubic) graphs __G__ that have a dominating cycle __C__ such that no other cycle __C__~1~ of __G__ satisfies __V(C)__ ⊆ __V__(__C__~1~). By a similar construction we obtain loopless 4‐regular graphs having precisely one hamiltonian cycle. The basis for these const
In 1975, John Sheehan conjectured that every Hamiltonian 4-regular graph has a second Hamiltonian cycle. Combined with earlier results this would imply that every Hamiltonian r-regular graph (r 3) has a second Hamiltonian cycle. We shall verify this for r 300.
Given r 3 3 and 1 s A s r, we determine all values of k for which every r-regular graph with edge-connectivity A has a k-factor. Some of the earliest results in graph theory are due to Petersen [8] and concern factors in graphs. Among others, Petersen proved that a regular graph of even degree has a
## Abstract Sufficient conditions on the degrees of a graph are given in order that its line graph have a hamiltonian cycle.