Note on edge-colored graphs and digraphs without properly colored cycles
| dc.creator | Gutin, Gregory | |
| dc.date | 2007-07-31 | |
| dc.date.accessioned | 2026-07-07T08:21:20Z | |
| dc.date.available | 2026-07-07T08:21:20Z | |
| dc.description | We study the following two functions: d(n,c) and $\vec{d}(n,c)$; d(n,c) ($\vec{d}(n,c)$) is the minimum number k such that every c-edge-colored undirected (directed) graph of order n and minimum monochromatic degree (out-degree) at least k has a properly colored cycle. Abouelaoualim et al. (2007) stated a conjecture which implies that d(n,c)=1. Using a recursive construction of c-edge-colored graphs with minimum monochromatic degree p and without properly colored cycles, we show that $d(n,c)\ge {1 \over c}(\log_cn -\log_c\log_cn)$ and, thus, the conjecture does not hold. In particular, this inequality significantly improves a lower bound on $\vec{d}(n,2)$ obtained by Gutin, Sudakov and Yeo in 1998. | |
| dc.identifier | https://arxiv.org/abs/0707.4580 | |
| dc.identifier | http://arxiv.org/abs/0707.4580 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135323 | |
| dc.subject | Discrete Mathematics | |
| dc.subject | G.2.2 | |
| dc.title | Note on edge-colored graphs and digraphs without properly colored cycles | |
| dc.type | text |