Induced matchings

Cameron, Kathie

doi:10.1016/0166-218x(92)90275-f

Cited by 231 publications

(170 citation statements)

References 9 publications

Supporting

Mentioning

166

Contrasting

Unclassified

Order By: Relevance

“…It has been known that the induced matching problem for a graph G can be reduced to the independent set problem for the square of line graph of G [15]. Indeed, the induced matching problem for many classes of graphs can be solved in this way [9], [15]- [18], [31], [32], [38].…”

Section: Induced Matchings and Strong Edge Coloringsmentioning

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%

“…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%

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

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.

show abstract

Section: Induced Matchings and Strong Edge Coloringsmentioning

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: Induced Matching and Strong Edge Coloring Problemmentioning

confidence: 99%

See 1 more Smart Citation

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

“…It is known to be NP-complete for planar graphs of maximum degree 4 [32], bipartite graphs of maximum degree 3, C 4 -free bipartite graphs [34], r-regular graphs for r ≥ 5, line-graphs, chair-free graphs, and Hamiltonian graphs [33] (among others). The problem is known to be polynomial time solvable for trees [22,42], chordal graphs [8], weakly chordal graphs [10], circular arc graphs [23], trapezoid graphs, interval-dimension graphs, and comparability graphs [24], interval-filament graphs, polygon-circle graphs, and ATfree graphs [9], (P 5 ,D m )-free graphs [33,35], (P k ,K 1,n )-free graphs [35], (bull, chair)-free graphs, line-graphs of Hamiltonian graphs [33], and graphs where the maximum matching and the maximum induced matching have the same size [33].…”

Section: Questionmentioning

confidence: 99%

The Parameterized Complexity of the Induced Matching Problem in Planar Graphs

Moser

Sikdar

Frontiers in Algorithmics

View full text Add to dashboard Cite

Given a graph G and an integer k ≥ 0, the NP-complete Induced Matching problem asks whether there exists an edge subset M of size at least k such that M is a matching and no two edges of M are joined by an edge of G. The complexity of this problem on general graphs as well as on many restricted graph classes has been studied intensively. However, other than the fact that the problem is W[1]-hard on general graphs little is known about the parameterized complexity of the problem in restricted graph classes. In this work, we provide first-time fixed-parameter tractability results for planar graphs, bounded-degree graphs, graphs with girth at least six, bipartite graphs, line graphs, and graphs of bounded treewidth. In particular, we give a linear-size problem kernel for planar graphs.

show abstract

“…If M is a matching, and the edge (i, j) ∈ M, we say that the nodes i and j are saturated by the edge (i, j). A matching M is acalled strong if every saturated node is adjacent to only one sturated node [12]. These strong or induced matchings in graphs have, in addition to theoretical importance, many practical significance, especially when the graph denotes the communication network [13].…”

Section: Introductionmentioning

confidence: 99%