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Algorithmic graph theory and perfect graphs
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This article is published in Order.The article was published on 1986-06-01. It has received 1324 citations till now. The article focuses on the topics: Trivially perfect graph & Perfect graph theorem.read more
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Fixed-parameter algorithms for Cochromatic Number and Disjoint Rectangle Stabbing via iterative localization
TL;DR: An algorithm with running time 2^O(^k^^^2^l^o^g^k^)n^O^(^1^) that solves the problem given a permutation @p of {1,...,n} and a positive integer k, thereby showing that it is fixed parameter tractable.
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On Metro-Line Crossing Minimization
TL;DR: This work considers the problem of drawing a set of simple paths along the edges of an embedded underlying graph G = (V;E) so that the total number of crossings among pairs of paths is minimized and examines several variations of the problem for which algorithms that yield optimal solutions are developed.
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Partially Complemented Representations of Digraphs
TL;DR: It is shown that given an adjacency-list representation of a digraph G, many fundamental graph algorithms can be carried out on any member G' of G's equivalence class in O(n+m) time, where m is the number of arcs in G, not the number in G' .
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Vertex-transitive CIS graphs
TL;DR: It is shown that a vertex-transitive graph is CIS if and only if it is well-covered, co-well- covered, and the product of its clique and stability numbers equals its order.
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Fractional coloring (orthogonal access) achieves all-unicast capacity (DoF) region of index coding (TIM) if and only if network topology is chordal
TL;DR: Fractional coloring (orthogonal access) achieves the all-unicast capacity (degrees of freedom (DoF)) region of the index coding (topological interference management (TIM) problem if and only if the bipartite network topology graph is chordal.
References
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Interval graphs and related topics
TL;DR: A more general paradigm for studying various classes of graphs is suggested which can be described as follows: when 9 is allowed to be an arbitrary family of sets, the class obtained as intersection graphs is all undirected graphs.