Clique Numbers of Graphs and Irreducible Exact m-Covers of Z
| dc.creator | Pan, Hao | |
| dc.creator | Zhao, Li-Lu | |
| dc.date | 2008-04-06 | |
| dc.date | 2008-04-26 | |
| dc.date.accessioned | 2026-07-07T09:35:07Z | |
| dc.date.available | 2026-07-07T09:35:07Z | |
| dc.description | For each m>=1 and k>=2, we construct a graph G=(V,E) with ω(G)=m such that max_{1\leq i\leq k} ω(G[V_i])=m for arbitrary partition V=V_1\cup...\cup V_k, where ω(G) is the clique number of G and G[V_i] is the induced subgraph of G with the vertex set V_i. Using this result, we show that for each m>=2 there exists an exact m-cover of Z which is not the union of two 1-covers. | |
| dc.description | 7 pages. Conjecture 3.1 in the first version has been solved | |
| dc.identifier | https://arxiv.org/abs/0804.0901 | |
| dc.identifier | http://arxiv.org/abs/0804.0901 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159729 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 05C30 (Primary); 11B25, 05C90, 05C20(Secondary) | |
| dc.title | Clique Numbers of Graphs and Irreducible Exact m-Covers of Z | |
| dc.type | text |