Vertex-edge domination in cubic graphs

被引：4
|
作者：
Ziemann, Radoslaw [1 ]
Zylinski, Pawel [1 ]
机构：
[1] Univ Gdansk, Fac Math Phys & Informat, PL-80308 Gdansk, Poland
来源：
DISCRETE MATHEMATICS | 2020年 / 343卷 / 11期
关键词：
vertex-edge domination; cubic graph; discharging method; linear programming; NUMBER;
D O I：
10.1016/j.disc.2020.112075
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We establish that any connected cubic graph of order n > 6 has a minimum vertex- edge dominating set of at most 10n/31 vertices, thus affirmatively answering the open question posed by Klostermeyer et al. in Discussiones Mathematicae Graph Theory, https://doi.org/10.7151/dmgt.2175. On the other hand, we present an infinite family of cubic graphs whose gamma(ve) ratio is equal to 2/7. Finally, we show that the problem of determining the minimum gamma(ve)-dominating set is NP-hard even in cubic planar graphs. (C) 2020 Elsevier B.V. All rights reserved.
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页数：14
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