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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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Towards A Unified View of Linear Structure on Graph Classes.
TL;DR: It is proved that LexBFS converges for a number of graph families, including interval graphs, cobipartite graphs, trees, and domino-free cocomparability graphs, as well as trees, which are the first non-trivial results of this kind.
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Greedy algorithms for tracking mobile users in special mobility graphs
TL;DR: The main contribution of this work is to propose algorithms to optimally solve the reporting center problem for vicinity 2 on interval graphs and for arbitrary vicinity on proper interval graphs.
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On the Size of Minimal Separators for Treedepth Decomposition
TL;DR: By the conjecture, there is a conjecture that there is an optimal treedepth decomposition even if one uses only minimal separators no larger than the treewidth of input graphs, and it is proved that the conjecture for many classes of graphs.
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Distributed localization using Levenberg-Marquardt algorithm
TL;DR: A distributed algorithm for sensor network localization based on a maximum likelihood formulation that relies on the Levenberg-Marquardt algorithm, which provides a good localization accuracy, and it converges to the same solution as its centralized counterpart.
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Directed Overlap-inclusion Graphs as Representations of Ciliate Genes
TL;DR: This paper introduces an extension of the framework of Brijder and Hoogeboom in terms of directed overlap-inclusion graphs where more of the linear structure of the ciliate genes is described and investigates a number of combinatorial properties of these graphs, including a necessary property interms of forbidden induced subgraphs.
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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.