Difference graphs

Hammer, Peter L.; Peled, Uri N.; Sun, Xuxu

doi:10.1016/0166-218x(90)90092-q

Cited by 101 publications

(70 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are several characterizations of P 5 -free bipartite graphs, see for example, Hammer et al [9], Chung et al [3] and Hujter and Tuza [10]. In particular, BP is a P 5 -free bipartite graph iff BP is bipartite and each connected component of BP is 2K 2 -free, i.e., its complement is C 4 -free.…”

Section: Complexity Resultsmentioning

confidence: 99%

Weighted Coloring on Planar, Bipartite and Split Graphs: Complexity and Improved Approximation

Werra

Demange

Escoffier

et al. 2004

Algorithms and Computation

View full text Add to dashboard Cite

Abstract. We study complexity and approximation of min weighted node coloring in planar, bipartite and split graphs. We show that this problem is NP-complete in planar graphs, even if they are trianglefree and their maximum degree is bounded above by 4. Then, we prove that min weighted node coloring is NP-complete in P8-free bipartite graphs, but polynomial for P5-free bipartite graphs. We next focus ourselves on approximability in general bipartite graphs and improve earlier approximation results by giving approximation ratios matching inapproximability bounds. We next deal with min weighted edge coloring in bipartite graphs. We show that this problem remains strongly NP-complete, even in the case where the input-graph is both cubic and planar. Furthermore, we provide an inapproximability bound of 7/6 − ε, for any ε > 0 and we give an approximation algorithm with the same ratio. Finally, we show that min weighted node coloring in split graphs can be solved by a polynomial time approximation scheme.

show abstract

Section: Complexity Resultsmentioning

confidence: 99%

Weighted Coloring on Planar, Bipartite and Split Graphs: Complexity and Improved Approximation

Werra

Demange

Escoffier

et al. 2004

Algorithms and Computation

View full text Add to dashboard Cite

show abstract

“…It is a bipartite graph known in the literature under various names such as difference graph [22] or chain graph [26]. The latter name is due to the fact that the neighborhoods of vertices in each part of the graph form a chain, i.e., the vertices can be linearly ordered under inclusion of their neighborhoods.…”

Section: Structural Characterization Of Bipartite Permutation and Unimentioning

confidence: 99%

Minimal Classes of Graphs of Unbounded Clique-Width

Lozin

2011

Ann. Comb.

View full text Add to dashboard Cite

show abstract

“…A bipartite graph G with bipartition (U, V) is called a chain graph if for any pair of vertices u, u ∈ U, either N(u) ⊆ N(u ) or N(u) ⊇ N(u ) (it is also known as a difference graph [33] and a Ferrers bigraph [34]). A disconnected graph consisting of k disjoint edges is denoted by kK 2 .…”

Section: Theorem II a Bipartite Graph Is A 2-dorg If And Only If It mentioning

confidence: 99%

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

Difference graphs

Cited by 101 publications

References 5 publications

Weighted Coloring on Planar, Bipartite and Split Graphs: Complexity and Improved Approximation

Weighted Coloring on Planar, Bipartite and Split Graphs: Complexity and Improved Approximation

Minimal Classes of Graphs of Unbounded Clique-Width

Dominating Sets and Induced Matchings in Orthogonal Ray Graphs

Contact Info

Product

Resources

About