Counting dominating sets in generalized series-parallel graphs

2019 ◽  
Vol 11 (06) ◽  
pp. 1950074
Author(s):  
Min-Sheng Lin
Keyword(s):  
Planar Graphs ◽  
Linear Time ◽  
Dominating Sets ◽  
Connected Dominating Sets ◽  
Complete Problem ◽  
Linear Time Algorithms

Counting dominating sets in a graph is a #P-complete problem even in planar graphs. This paper studies this problem for generalized series-parallel graphs, which are a subclass of planar graphs. This work develops some linear-time algorithms for counting dominating sets and their two variants, independent dominating sets and connected dominating sets in generalized series-parallel graphs.

Fast and simple algorithms for counting dominating sets in distance-hereditary graphs

2020 ◽  
pp. 2150012
Author(s):  
Min-Sheng Lin
Keyword(s):  
Linear Time ◽  
Bipartite Graphs ◽  
Chordal Graphs ◽  
Dominating Sets ◽  
Complete Problem ◽  
Split Graphs ◽  
Linear Time Algorithms ◽  
Chordal Bipartite Graphs

Counting dominating sets (DSs) in a graph is a #P-complete problem even for chordal bipartite graphs and split graphs, which are both subclasses of weakly chordal graphs. This paper investigates this problem for distance-hereditary graphs, which is another known subclass of weakly chordal graphs. This work develops linear-time algorithms for counting DSs and their two variants, total DSs and connected DSs in distance-hereditary graphs.

New Linear-Time Algorithms for Edge-Coloring Planar Graphs

Algorithmica ◽  
2007 ◽  
Vol 50 (3) ◽  
pp. 351-368 ◽  
Author(s):  
Richard Cole ◽  
Łukasz Kowalik
Keyword(s):  
Planar Graphs ◽  
Linear Time ◽  
Edge Coloring ◽  
Linear Time Algorithms

LINEAR-TIME ALGORITHMS FOR DISJOINT TWO-FACE PATHS PROBLEMS IN PLANAR GRAPHS

1996 ◽  
Vol 07 (02) ◽  
pp. 95-110 ◽  
Author(s):  
HEIKE RIPPHAUSEN-LIPA ◽  
DOROTHEA WAGNER ◽  
KARSTEN WEIHE
Keyword(s):  
Planar Graphs ◽  
Linear Time ◽  
Time Algorithm ◽  
Disjoint Paths ◽  
Linear Time Algorithm ◽  
Vertex Disjoint ◽  
Linear Time Algorithms

In this paper we present a linear-time algorithm for the vertex-disjoint Two-Face Paths Problem in planar graphs, i.e., the problem of finding k vertex-disjoint paths between pairs of terminals which lie on two face boundaries. The algorithm is based on the idea of finding rightmost paths with a certain property in planar graphs. Using this method, a linear-time algorithm for finding vertex-disjoint paths of a prescribed homotopy is derived. Moreover, the algorithm is modified to solve the more general linkage problem in linear time, as well.

Linear-time algorithms for problems on planar graphs with fixed disk dimension

2007 ◽  
Vol 101 (1) ◽  
pp. 36-40
Author(s):  
Faisal N. Abu-Khzam ◽  
Michael A. Langston
Keyword(s):  
Planar Graphs ◽  
Linear Time ◽  
Linear Time Algorithms
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