On the Number of Connected Sets in Bounded Degree Graphs

被引：4

作者：

Kangas, Kustaa ^{[1
]}

Kaski, Petteri ^{[2
]}

Koivisto, Mikko ^{[1
]}

Korhonen, Janne H. ^{[1
]}

机构：

[1] Univ Helsinki, Dept Comp Sci, HIIT, POB 68, Helsinki 00014, Finland

[2] Aalto Univ, HIIT, Dept Informat & Comp Sci, POB 15400, Aalto 00076, Finland

来源：

GRAPH-THEORETIC CONCEPTS IN COMPUTER SCIENCE | 2014年 / 8747卷

基金：

芬兰科学院; 欧盟地平线“2020”; 欧洲研究理事会;

关键词：

INDEPENDENT SETS;

D O I：

10.1007/978-3-319-12340-0_28

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A set of vertices in a graph is connected if the set induces a connected subgraph. Using Shearer's entropy lemma, we show that the number of connected sets in an n-vertex graph with maximum vertex degree d is O(1.9351(n)) for d = 3, O(1.9812(n)) for d = 4, and O(1.9940(n)) for d = 5. Dually, we construct infinite families of generalized ladder graphs whose number of connected sets is bounded from below by Omega(1.5537(n)) for d = 3, Omega(1.6180(n)) for d = 4, and Omega(1.7320(n)) for d = 5.

引用

页码：336 / 347

页数：12

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