𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A circular graph — counterexample to the Duchet kernel conjecture

✍ Scribed by A. Apartsin; E. Ferapontova; V. Gurvich

Book ID
108316225
Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
141 KB
Volume
178
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

A corrected version of the Duchet kernel
A corrected version of the Duchet kernel conjecture
✍ E. Boros; V. Gurvich 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 146 KB

In 1980, Piere Duchet conjectured that odd-directed cycles are the only edge minimal kernel-less connected digraphs, i.e. in which after the removal of any edge a kernel appears. Although this conjecture was disproved recently by Apartsin et al. (1996), the following modification of Duchet's conject

A counterexample to a conjecture on the
A counterexample to a conjecture on the bondage number of a graph
✍ Ulrich Teschner 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 113 KB

The bondage number h(G) of a nonempty graph G was first introduced by Fink, Jacobson, Kinch and Roberts in [3]. They generalized a former approach to domination-critical graphs, In their publication they conjectured that b(G)<d(G)+ 1 for any nonempty graph G.

A counterexample to the bold conjecture
A counterexample to the bold conjecture
✍ Sakuma, Tadashi 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 83 KB 👁 1 views

A pair of vertices (x, y) of a graph G is an ω-critical pair if ω(G + xy) > ω(G), where G + xy denotes the graph obtained by adding the edge xy to G and ω(H) is the clique number of H. The ω-critical pairs are never edges in G. A maximal stable set S of G is called a forced color class of G if S mee