A Remark on Triangle-Critical Graphs
| dc.creator | Pedersen, Anders Sune | |
| dc.date | 2008-02-24 | |
| dc.date.accessioned | 2026-07-07T09:22:58Z | |
| dc.date.available | 2026-07-07T09:22:58Z | |
| dc.description | A connected $k$-chromatic graph $G$ with $k \geq 3$ is said to be triangle-critical, if every edge of $G$ is contained in an induced triangle of $G$ and the removal of any triangle from $G$ decreases the chromatic number of $G$ by three. B. Toft posed the problem of showing that the complete graphs on more than two vertices are the only triangle-critical graphs. By applying a method of M. Stiebitz [Discrete Math. 64 (1987), 91--93], we answer the problem affirmatively for triangle-critical $k$-chromatic graphs with $k \leq 6$. | |
| dc.identifier | https://arxiv.org/abs/0802.3529 | |
| dc.identifier | http://arxiv.org/abs/0802.3529 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155567 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C05 | |
| dc.title | A Remark on Triangle-Critical Graphs | |
| dc.type | text |