scholarly journals Recognizing Outer 1-Planar Graphs in Linear Time

2013 ◽  
pp. 107-118 ◽  
Author(s):  
Christopher Auer ◽  
Christian Bachmaier ◽  
Franz J. Brandenburg ◽  
Andreas Gleißner ◽  
Kathrin Hanauer ◽  
...  
Keyword(s):  
Planar Graphs ◽  
Linear Time

scholarly journals Linear-Time Succinct Encodings of Planar Graphs via Canonical Orderings

1999 ◽  
Vol 12 (3) ◽  
pp. 317-325 ◽  
Author(s):  
Xin He ◽  
Ming-Yang Kao ◽  
Hsueh-I Lu
Keyword(s):  
Planar Graphs ◽  
Linear Time

scholarly journals Planar graphs, negative weight edges, shortest paths, and near linear time

2006 ◽  
Vol 72 (5) ◽  
pp. 868-889 ◽  
Author(s):  
Jittat Fakcharoenphol ◽  
Satish Rao
Keyword(s):  
Planar Graphs ◽  
Linear Time ◽  
Shortest Paths ◽  
Negative Weight

Edge-Disjoint (s,t)-Paths in Undirected Planar Graphs in Linear Time

1997 ◽  
Vol 23 (1) ◽  
pp. 121-138 ◽  
Author(s):  
Karsten Weihe
Keyword(s):  
Planar Graphs ◽  
Linear Time ◽  
Edge Disjoint

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.

Finding Double Euler Trails of Planar Graphs in Linear Time

2002 ◽  
Vol 31 (4) ◽  
pp. 1255-1285 ◽  
Author(s):  
Zhi-Zhong Chen ◽  
Xin He ◽  
Chun-Hsi Huang
Keyword(s):  
Planar Graphs ◽  
Linear Time

On the Complexity of Reverse Minus and Signed Domination on Graphs

2015 ◽  
Vol 15 (01n02) ◽  
pp. 1550008
Author(s):  
CHUAN-MIN LEE ◽  
CHENG-CHIEN LO
Keyword(s):  
Planar Graphs ◽  
Decision Problem ◽  
Linear Time ◽  
Point Of View ◽  
Chordal Graphs ◽  
Fixed Parameter Tractable ◽  
Signed Domination ◽  
Domination Problem ◽  
Np Complete ◽  
Domination Problems

Motivated by the concept of reverse signed domination, we introduce the reverse minus domination problem on graphs, and study the reverse minus and signed domination problems from the algorithmic point of view. In this paper, we show that both the reverse minus and signed domination problems are polynomial-time solvable for strongly chordal graphs and distance-hereditary graphs, and are linear-time solvable for trees. For chordal graphs and bipartite planar graphs, however, we show that the decision problem corresponding to the reverse minus domination problem is NP-complete. For doubly chordal graphs and bipartite planar graphs, we show that the decision problem corresponding to the reverse signed domination problem is NP-complete. Furthermore, we show that even when restricted to bipartite planar graphs or doubly chordal graphs, the reverse signed domination problem is not fixed parameter tractable.

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