Enabling distributed throughput maximization in wireless mesh networks: a partitioning approach
Proceedings of the 12th annual international conference on Mobile computing and networking
The impact of imperfect scheduling on cross-layer congestion control in wireless networks
IEEE/ACM Transactions on Networking (TON)
Claw-free graphs. III. Circular interval graphs
Journal of Combinatorial Theory Series B
Claw-free graphs. V. Global structure
Journal of Combinatorial Theory Series B
Analyzing the performance of greedy maximal scheduling via local pooling and graph theory
INFOCOM'10 Proceedings of the 29th conference on Information communications
Analyzing the performance of greedy maximal scheduling via local pooling and graph theory
IEEE/ACM Transactions on Networking (TON)
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Strongly perfect graphs have been studied by several authors (e.g. Berge and Duchet (1984) [1], Ravindra (1984) [12] and Wang (2006) [14]). In a series of two papers, the current paper being the first one, we investigate a fractional relaxation of strong perfection. Motivated by a wireless networking problem, we consider claw-free graphs that are fractionally strongly perfect in the complement. We obtain a forbidden induced subgraph characterization and display graph-theoretic properties of such graphs. It turns out that the forbidden induced subgraphs that characterize claw-free graphs that are fractionally strongly perfect in the complement are precisely the cycle of length 6, all cycles of length at least 8, four particular graphs, and a collection of graphs that are constructed by taking two graphs, each a copy of one of three particular graphs, and joining them in a certain way by a path of arbitrary length. Wang (2006) [14] gave a characterization of strongly perfect claw-free graphs. As a corollary of the results in this paper, we obtain a characterization of claw-free graphs whose complements are strongly perfect.