101 research outputs found
Detecting 2-joins faster
2-joins are edge cutsets that naturally appear in the decomposition of
several classes of graphs closed under taking induced subgraphs, such as
balanced bipartite graphs, even-hole-free graphs, perfect graphs and claw-free
graphs. Their detection is needed in several algorithms, and is the slowest
step for some of them. The classical method to detect a 2-join takes
time where is the number of vertices of the input graph and the number
of its edges. To detect \emph{non-path} 2-joins (special kinds of 2-joins that
are needed in all of the known algorithms that use 2-joins), the fastest known
method takes time . Here, we give an -time algorithm for both
of these problems. A consequence is a speed up of several known algorithms
Algorithms for square-3PC(·, ·)-free Berge graphs
We consider the class of graphs containing no odd hole, no odd antihole, and no configuration consisting of three paths between two nodes such that any two of the paths
induce a hole, and at least two of the paths are of length 2. This class generalizes clawfree Berge graphs and square-free Berge graphs. We give a combinatorial algorithm of
complexity O(n7) to find a clique of maximum weight in such a graph. We also consider several subgraph-detection problems related to this class
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