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An 11-vertex theorem for 3-connected cubic graphs

✍ Scribed by R. E. L. Aldred; BauSheng; D. A. Holton; Gordon F. Royle

Publisher: John Wiley and Sons
Year: 1988
Tongue: English
Weight: 451 KB
Volume: 12
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190120412

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper w e determine the circumstances under which a set of 11 vertices in a 3-connected cubic graph lies on a cycle. In addition, w e consider the number of such cycles that exist and characterize those graphs in which a set of 9 vertices lies in exactly two cycles.

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✍ Vincenzo Auletta; Yefim Dinitz; Zeev Nutov; Domenico Parente 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 71 KB

The problem of finding a minimum weight k-vertex connected spanning sub-Ž . graph in a graph G s V, E is considered. For k G 2, this problem is known to be NP-hard. Combining properties of inclusion-minimal k-vertex connected graphs Ž and of k-out-connected graphs i.e., graphs which contain a vertex