Counterexamples to a conjecture of Merker on 3-connected cubic planar graphs with a large cycle spectrum gap

被引：1
|
作者：
Zamfirescu, Carol T. [1 ,2 ]
机构：
[1] Univ Ghent, Dept Appl Math Comp Sci & Stat, Krijgslaan 281 S9, B-9000 Ghent, Belgium
[2] Babe Bolyai Univ, Dept Math, Cluj Napoca, Romania
来源：
DISCRETE MATHEMATICS | 2022年 / 345卷 / 06期
关键词：
Cycles; Cycle spectrum; 3-connected; Cubic; Planar graphs;
D O I：
10.1016/j.disc.2022.112824
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Merker conjectured that if k >= 2 is an integer and G a 3-connected cubic planar graph of circumference at least k, then the set of cycle lengths of G must contain at least one element of the interval [k, 2k + 2]. We here prove that for every even integer k >= 6 there is an infinite family of counterexamples. (c) 2022 Elsevier B.V. All rights reserved.
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