## Abstract In 1960, Dirac posed the conjecture that __r__‐connected 4‐critical graphs exist for every __r__ ≥ 3. In 1989, Erdős conjectured that for every __r__ ≥ 3 there exist __r__‐regular 4‐critical graphs. In this paper, a technique of constructing __r__‐regular __r__‐connected vertex‐transiti
Stability Critical Graphs and Even Subdivisions of K4
✍ Scribed by E.C. Sewell; L.E. Trotter
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 375 KB
- Volume
- 59
- Category
- Article
- ISSN
- 0095-8956
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📜 SIMILAR VOLUMES
A k-critical (multi-) graph G has maximum degree k, chromatic index χ (G) = k + 1, and χ (G -e) < k + 1 for each edge e of G. For each k ≥ 3, we construct k-critical (multi-) graphs with certain properties to obtain counterexamples to some well-known conjectures.
## Abstract It is proved that for every positive integers __k__, __r__ and __s__ there exists an integer __n__ = __n__(__k__,__r__,__s__) such that every __k__‐connected graph of order at least __n__ contains either an induced path of length __s__ or a subdivision of the complete bipartite graph __
An odd hole in a graph is an induced cycle of odd length at least five. In this article we show that every imperfect K 4 -free graph with no odd hole either is one of two basic graphs, or has an even pair or a clique cutset. We use this result to show that every K 4 -free graph with no odd hole has