Graphs having circuits with at least two chords
نویسندگان
چکیده
منابع مشابه
Chords of longest circuits in locally planar graphs
It was conjectured by Thomassen ([B. Alspach, C. Godsil, Cycle in graphs, Ann. Discrete Math. 27 (1985)], p. 466) that every longest circuit of a 3-connected graph must have a chord. This conjecture is verified for locally 4-connected planar graphs, that is, let N be the set of natural numbers; then there is a function h : N → N such that, for every 4-connected graph G embedded in a surface S w...
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متن کاملChords of longest circuits in 3-connected graphs
Thomassen conjectured that every longest circuit of a 3-connected graph has a chord. The conjecture is veri2ed in this paper for projective planar graphs with minimum degree at least 4. c © 2002 Elsevier Science B.V. All rights reserved.
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We characterize all simple graphs such that each edge is a chord of some cycle. As a consequence, we characterize all simple 2-connected graphs such that, for any two adjacent vertices x and y, the local connectivity k(x, y) ≥ 3. We also make a conjecture about chords for 3-connected graphs.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1982
ISSN: 0095-8956
DOI: 10.1016/0095-8956(82)90004-1