The Circular Chromatic Number of the Mycielskian of Mt(Kn)
| dc.creator | Ma, Zuqiang | |
| dc.creator | Cai, Junliang | |
| dc.date | 2009-01-15 | |
| dc.date.accessioned | 2026-07-07T12:29:41Z | |
| dc.date.available | 2026-07-07T12:29:41Z | |
| dc.description | As a natural generalization of chromatic number of a graph, the circular chromatic number of graphs (or the star chromatic number) was introduced by A.Vince in 1988. Let $M^t(G)$ denote the $t$th iterated Mycielski graph of $G$. It was conjectured by Chang, Huang and Zhu(Discrete mathematics,205(1999), 23-37) that for all $n \ge t+2, χ_c(M^t(K_n))=χ(M^t(K_n))=n+t.$ In 2004, D.D.F. Liu proved the conjecture when $t\ge 2$, $n\ge 2^{t-1}+2t-2$. In this paper,we show that the result can be strengthened to the following: if $t\ge 4$, $n\ge {11/12}2^{t-1}+2t+{1/3}$, then $χ_c(M^t(K_n))=χ(M^t(K_n))$. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0901.2259 | |
| dc.identifier | http://arxiv.org/abs/0901.2259 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215959 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A30 | |
| dc.title | The Circular Chromatic Number of the Mycielskian of Mt(Kn) | |
| dc.type | text |