Name
Abstract | ||
|---|---|---|
Let G be a graph of order n>=3. An even squared Hamiltonian cycle (ESHC) of G is a Hamiltonian cycle C=v"1v"2...v"nv"1 of G with chords v"iv"i"+"3 for all [email protected][email protected]?n (where v"n"+"j=v"j for j>=1). When n is even, an ESHC contains all bipartite 2-regular graphs of order n. We prove that there is a positive integer N such that for every graph G of even order n>=N, if the minimum degree is @d(G)>=n2+92, then G contains an ESHC. We show that the condition of n being even cannot be dropped and the constant 92 cannot be replaced by 1. Our results can be easily extended to evenkth powered Hamiltonian cycles for all k>=2. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.disc.2011.12.013 | Discrete Mathematics |
Keywords | Field | DocType |
dirac theorem,hamiltonian cycle,posa's conjecture | Integer,Discrete mathematics,Graph,Combinatorics,Square (algebra),Hamiltonian (quantum mechanics),Hamiltonian path,Bipartite graph,Chord (music),Mathematics | Journal |
Volume | Issue | ISSN |
312 | 6 | 0012-365X |
Citations | PageRank | References |
0 | 0.34 | 11 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| G. Chen | 1 | 32 | 8.36 |
| Katsuhiro Ota | 2 | 404 | 56.84 |
| Akira Saito | 3 | 361 | 64.55 |
| Yi Zhao | 4 | 88 | 10.43 |