Chords of longest circuits in locally planar graphs
نویسندگان
چکیده
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 with Euler genus g and face-width at least h(g), every longest circuit of G has a chord. c © 2005 Elsevier Ltd. All rights reserved.
منابع مشابه
Chords 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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ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 28 شماره
صفحات -
تاریخ انتشار 2007