Maximal independent sets in caterpillar graphs

被引：10

作者：

Ortiz, Carmen ^{[2
]}

Villanueva, Monica ^{[1
]}

机构：

[1] Univ Santiago Chile, Fac Engn, Santiago, Chile

[2] Adolfo Ibanez Univ, Fac Sci & Engn, Santiago, Chile

来源：

DISCRETE APPLIED MATHEMATICS | 2012年 / 160卷 / 03期

关键词：

Graph algorithms; Caterpillar graph; Enumeration of maximal independent sets; Intersection graph; Independent graph; Clique graph; NUMBER; ALGORITHM; GENERATE; FAMILY;

D O I：

10.1016/j.dam.2011.10.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A caterpillar graph is a tree in which the removal of all pendant vertices results in a chordless path. In this work, we determine the number of maximal independent sets (mis) in caterpillar graphs. For a general graph, this problem is #P-complete. We provide a polynomial time algorithm to generate the whole family of mis in a caterpillar graph. We also characterize the independent graph (intersection graph of mis) and the clique graph (intersection graph of cliques) of complete caterpillar graphs. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：259 / 266

页数：8

共 50 条

[31] Minimum connected dominating sets and maximal independent sets in unit disk graphs
Wu, WL
Du, HW
Jia, XH
Li, YS
Huang, SCH
THEORETICAL COMPUTER SCIENCE, 2006, 352 (1-3) : 1 - 7
[32] Maximal and maximum independent sets in graphs with at most r cycles
Sagan, Bruce E.
Vatter, Vincent R.
JOURNAL OF GRAPH THEORY, 2006, 53 (04) : 283 - 314
[33] Distinct sizes of maximal independent sets on graphs with restricted girth
Cappelle, Marcia
Nascimento, Julliano
Santos, Vinicius
RAIRO-OPERATIONS RESEARCH, 2024, 58 (03) : 2379 - 2391
[34] DISJOINT CLIQUES AND DISJOINT MAXIMAL INDEPENDENT SETS OF VERTICES IN GRAPHS
ERDOS, P
HOBBS, AM
PAYAN, C
DISCRETE MATHEMATICS, 1982, 42 (01) : 57 - 61
[35] ON MAXIMAL INDEPENDENT SETS OF VERTICES IN CLAW-FREE GRAPHS
MINTY, GJ
JOURNAL OF COMBINATORIAL THEORY SERIES B, 1980, 28 (03) : 284 - 304
[36] The maximum number of maximal independent sets in unicyclic connected graphs
Koh, K. M.
Goh, C. Y.
Dong, F. M.
DISCRETE MATHEMATICS, 2008, 308 (17) : 3761 - 3769
[37] The second largest number of maximal independent sets in twinkle graphs
Lin, Jenq-Jong
Jou, Min-Jen
Journal of Combinatorial Mathematics and Combinatorial Computing, 2020, 113 : 31 - 48
[38] All Maximal Independent Sets and Dynamic Dominance for Sparse Graphs
Eppstein, David
PROCEEDINGS OF THE SIXTEENTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, 2005, : 451 - 459
[39] THE NUMBER OF MAXIMAL INDEPENDENT SETS IN TRIANGLE-FREE GRAPHS
HUJTER, M
TUZA, Z
SIAM JOURNAL ON DISCRETE MATHEMATICS, 1993, 6 (02) : 284 - 288
[40] On the number of maximal independent sets in minimum colorings of split graphs
Bresar, Bostjan
Movarraei, Nazanin
DISCRETE APPLIED MATHEMATICS, 2018, 247 : 352 - 356

← 1 2 3 4 5 →