On properly colored hamiltonian cycles in cubes of Distance-Colored Grids
| dc.contributor.author | Dogan D. | |
| dc.contributor.author | Kolasinski K. | |
| dc.contributor.author | Zhang P. | |
| dc.date.accessioned | 2019-10-26T21:36:09Z | |
| dc.date.available | 2019-10-26T21:36:09Z | |
| dc.date.issued | 2013 | |
| dc.department | Ege Üniversitesi | en_US |
| dc.description.abstract | For a connected graph G and a positive integer k, the kth power Gkof G is the graph with V (Gk) = V (G) where uv ? E(Gk) if the distance dG(u, v) between u and v is at most k. The edge coloring of Gk defined by assigning each edge uv of Gk the color dG(u, v) produces an edge-colored graph Gk called a distance-colored graph. A distance-colored graph Gk is Hamiltonian-colored if Gk contains a properly colored Hamiltonian cycle. For a grid G = Pn Pm with n, m ? 2, it is known that G3 is Hamiltonian-colored and that G2 is Hamiltonian-colored if and only if nm ? 0 (mod 4). It is shown here that (i) G3 contains a properly colored Hamiltonian cycle whose edges are colored only 1 or 3 if and only if nm is even unless n = m = 2 or {n, m} is {2, 3} or {2, 7} and (ii) G3 contains a properly colored Hamiltonian cycle whose edges are colored only 2 or 3 if and only if nm ? 0 (mod 4) unless n = m = 2. | en_US |
| dc.identifier.endpage | 67 | en_US |
| dc.identifier.issn | 0972-8600 | |
| dc.identifier.issn | 0972-8600 | en_US |
| dc.identifier.issue | 1 | en_US |
| dc.identifier.scopusquality | Q3 | en_US |
| dc.identifier.startpage | 57 | en_US |
| dc.identifier.uri | https://hdl.handle.net/11454/17987 | |
| dc.identifier.volume | 10 | en_US |
| dc.indekslendigikaynak | Scopus | en_US |
| dc.language.iso | en | en_US |
| dc.relation.ispartof | AKCE International Journal of Graphs and Combinatorics | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Distance-colored graph | en_US |
| dc.subject | Hamiltonian-colored graph | en_US |
| dc.subject | Powers of a graph | en_US |
| dc.title | On properly colored hamiltonian cycles in cubes of Distance-Colored Grids | en_US |
| dc.type | Article | en_US |
