On distance-3 matchings and induced matchings
Discrete Applied Mathematics
Hybrid tractability of valued constraint problems
Artificial Intelligence
Maximum weight independent sets in hole- and dart-free graphs
Discrete Applied Mathematics
Maximum regular induced subgraphs in 2P3-free graphs
Theoretical Computer Science
On atomic structure of P5-free subclasses and Maximum Weight Independent Set problem
Theoretical Computer Science
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We present the first polynomial-time algorithm to solve the maximum weight independent set problem for apple-free graphs, which is a common generalization of several important classes where the problem can be solved efficiently, such as claw-free graphs, chordal graphs, and cographs. Our solution is based on a combination of two algorithmic techniques (modular decomposition and decomposition by clique separators) and a deep combinatorial analysis of the structure of apple-free graphs. Our algorithm is robust in the sense that it does not require the input graph $G$ to be apple-free; the algorithm either finds an independent set of maximum weight in $G$ or reports that $G$ is not apple-free.