PACKING AND COVERING BALLS IN GRAPHS EXCLUDING A MINOR

被引：1

作者：

Bousquet, Nicolas ^{[1
]}

Van Batenburg, Wouter Cames ^{[2
]}

Esperet, Louis ^{[1
]}

Joret, Gwenael ^{[2
]}

Lochet, William ^{[3
]}

Muller, Carole ^{[4
]}

Pirot, Francois ^{[1
,2
]}

机构：

[1] Univ Grenoble Alpes, Lab G SCOP, CNRS, Grenoble, France

[2] Univ Libre Bruxelles, Dept Informat, Brussels, Belgium

[3] Univ Bergen, Algorithms Res Grp, Bergen, Norway

[4] Univ Libre Bruxelles, Dept Math, Brussels, Belgium

来源：

COMBINATORICA | 2021年 / 41卷 / 03期

关键词：

05C10; 05C12; 05C65; 05C69; 05C83;

D O I：

10.1007/s00493-020-4423-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that for every integer t > 1 there exists a constant c(t) such that for every K-t-minor-free graph G, and every set S of balls in G, the minimum size of a set of vertices of G intersecting all the balls of S is at most c(t) times the maximum number of vertex-disjoint balls in S. This was conjectured by Chepoi, Estellon, and Vaxes in 2007 in the special case of planar graphs and of balls having the same radius.

引用

页码：299 / 318

页数：20

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