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.
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页码：336 / 347
页数：12
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