Induced matchings in asteroidal triple-free graphs

Chang, Jou–Ming

doi:10.1016/s0166-218x(03)00390-1

Cited by 44 publications

(33 citation statements)

References 26 publications

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“…The induced matching problem is NP-hard for general bipartite graphs [15], [54], and even for unit grid intersection graphs [45], whereas the problem can be solved in O(n + m) time for bipartite permutation graphs [18], in O(n 2 ) time for convex graphs [8], in O(nm) time for interval bigraphs [1], and in O(m 3 ) time for chordal bipartite graphs [1], [17], [22]. Also, the weighted induced matching problem can be solved in O(m 4 ) time for chordal bipartite graphs [17].…”

Section: Induced Matching and Strong Edge Coloring Problemmentioning

confidence: 99%

“…Indeed, the induced matching problem for many classes of graphs can be solved in this way [9], [15]- [18], [31], [32], [38]. The square of line…”

Section: Induced Matchings and Strong Edge Coloringsmentioning

confidence: 99%

“…For cocomparability graphs, the independent set problem can be solved in linear time [41], and the coloring problem can be solved in O(n 3 ) time [30]. [18] if for every e ∈ F, the edges in F \ {e} are contained in the same connected component of G − N[e]. We can see that every edge-asteroidal set is an induced matching, and a set of two edges is an edge-asteroidal set if it forms 2K 2 .…”

Section: Lemma 10 For Any Edge E In a Graph Gmentioning

confidence: 99%

“…We can see that every edge-asteroidal set is an induced matching, and a set of two edges is an edge-asteroidal set if it forms 2K 2 . The maximum cardinality of an edge-asteroidal set in G is called the asteroidal index of G. The following is shown in [18].…”

Section: Lemma 10 For Any Edge E In a Graph Gmentioning

confidence: 99%

See 3 more Smart Citations

Dominating Sets and Induced Matchings in Orthogonal Ray Graphs

Takaoka

Tayu

Ueno

2014

IEICE Trans. Inf. & Syst.

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Asahi TAKAOKA†a) , Student Member, Satoshi TAYU †b) , Member, and Shuichi UENO †c) , Fellow SUMMARY An orthogonal ray graph is an intersection graph of horizontal and vertical rays (closed half-lines) in the plane. Such a graph is 3-directional if every vertical ray has the same direction, and 2-directional if every vertical ray has the same direction and every horizontal ray has the same direction. We derive some structural properties of orthogonal ray graphs, and based on these properties, we introduce polynomial-time algorithms that solve the dominating set problem, the induced matching problem, and the strong edge coloring problem for these graphs. We show that for 2-directional orthogonal ray graphs, the dominating set problem can be solved in O(n 2 log 5 n) time, the weighted dominating set problem can be solved in O(n 4 log n) time, and the number of dominating sets of a fixed size can be computed in O(n 6 log n) time, where n is the number of vertices in the graph. We also show that for 2-directional orthogonal ray graphs, the weighted induced matching problem and the strong edge coloring problem can be solved in O(n 2 + m log n) time, where m is the number of edges in the graph. Moreover, we show that for 3-directional orthogonal ray graphs, the induced matching problem can be solved in O(m 2 ) time, the weighted induced matching problem can be solved in O(m 4 ) time, and the strong edge coloring problem can be solved in O(m 3 ) time. We finally show that the weighted induced matching problem can be solved in O(m 6 ) time for orthogonal ray graphs.

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Section: Induced Matching and Strong Edge Coloring Problemmentioning

confidence: 99%

“…Indeed, the induced matching problem for many classes of graphs can be solved in this way [9], [15]- [18], [31], [32], [38]. The square of line…”

Section: Induced Matchings and Strong Edge Coloringsmentioning

confidence: 99%

Section: Lemma 10 For Any Edge E In a Graph Gmentioning

confidence: 99%

Section: Lemma 10 For Any Edge E In a Graph Gmentioning

confidence: 99%

See 2 more Smart Citations

Dominating Sets and Induced Matchings in Orthogonal Ray Graphs

Takaoka

Tayu

Ueno

2014

IEICE Trans. Inf. & Syst.

View full text Add to dashboard Cite

show abstract

“…However, this problem has been shown to be solvable in polynomial time for several graph classes [17,18,19,20,21,52,53,64,73,74] and even in linear time for trees [49,53,122].…”

Section: Induced Matchingsmentioning

confidence: 99%