Graph classes: a survey
Fully dynamic algorithms for chordal graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A Fully Dynamic Algorithm for Recognizing and Representing Proper Interval Graphs
SIAM Journal on Computing
A fully dynamic algorithm for modular decomposition and recognition of cographs
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
An Optimal Parallel Co-Connectivity Algorithm
Theory of Computing Systems
Characterizing and Computing Minimal Cograph Completions
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Dynamically maintaining split graphs
Discrete Applied Mathematics
Minimum fill-in and treewidth of split+ke and split+kv graphs
Discrete Applied Mathematics
Characterizing and computing minimal cograph completions
Discrete Applied Mathematics
Minimum fill-in and treewidth of split+ke and split+kv graphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
A novel branching strategy for parameterized graph modification problems
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
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In this paper, we establish structural properties of cographs which enable us to present an algorithm which, for a cograph G and a non-edge xy (i.e., two non-adjacent vertices x and y) of G, finds the minimum number of edges that need to be added to the edge set of G such that the resulting graph is a cograph and contains the edge xy. The motivation for this problem comes from algorithms for the dynamic recognition and online maintenance of graphs; the proposed algorithm could be a suitable addition to the algorithm of Shamir and Sharan [13] for the online maintenance of cographs. The proposed algorithm runs in time linear in the size of the input graph and requires linear space.