A LINEAR-TIME ALGORITHM FOR FINDING A COMPLETE GRAPH MINOR IN A DENSE GRAPH

被引：1

作者：

Dujmovic, Vida ^{[1
]}

Harvey, Daniel J. ^{[2
]}

Joret, Gwenael ^{[3
]}

Reed, Bruce ^{[4
,5
]}

Wood, David R. ^{[6
]}

机构：

[1] Univ Ottawa, Sch Elect Engn & Comp Sci, Ottawa, ON, Canada

[2] Univ Melbourne, Dept Math & Stat, Melbourne, Vic, Australia

[3] Univ Libre Brussels, Dept Informat, B-1050 Brussels, Belgium

[4] McGill Univ, Sch Comp Sci, Montreal, PQ, Canada

[5] Natl Inst Informat, Kunitachi, Japan

[6] Monash Univ, Sch Math Sci, Melbourne, Vic 3004, Australia

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2013年 / 27卷 / 04期

基金：

加拿大自然科学与工程研究理事会; 澳大利亚研究理事会;

关键词：

EXTREMAL FUNCTION; PATHS;

D O I：

10.1137/120866725

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let g(t) be the minimum number such that every graph G with average degree d(G) >= g(t) contains a K-t-minor. Such a function is known to exist, as originally shown by Mader. Kostochka and Thomason independently proved that g(t) is an element of Theta(t root log t). This paper shows that for all fixed epsilon > 0 and fixed sufficiently large t >= t(epsilon), if d(G) >= (2 + epsilon) g(t), then we can find this K-t-minor in linear time. This improves a previous result by Reed and Wood who gave a linear-time algorithm when d(G) >= 2(t-2).

引用

页码：1770 / 1774

页数：5

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