Discrete Mathematics - Topics on domination
Domination numbers of planar graphs
Journal of Graph Theory
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A fast algorithm for the maximum clique problem
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
Algorithmic aspects of constrained unit disk graphs
Algorithmic aspects of constrained unit disk graphs
Robust algorithms for restricted domains
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Constructing Minimum Connected Dominating Sets with Bounded Diameters in Wireless Networks
IEEE Transactions on Parallel and Distributed Systems
Clique Relaxations in Social Network Analysis: The Maximum k-Plex Problem
Operations Research
On the maximum quasi-clique problem
Discrete Applied Mathematics
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This paper studies distance-based clique relaxations in unit disk graphs arising in wireless networking applications. Namely, a 2-clique is a subset of nodes with pairwise distance at most two in the graph, and a 2-club is a subset of nodes inducing a subgraph of diameter two. It is shown that in a unit disk graph any 2-clique is 4-dominated and any 2-club is 3-dominated. The former observation is used to develop a 12-approximation algorithm for the maximum 2-clique problem in unit disk graphs. Moreover, this also implies polynomial solvability of the minimum dominating set problem in unit disk graphs of diameter two, whereas the same problem is shown to be hard in general diameter-two graphs. The paper also poses several related open questions of interest.