Algorithms for Square-3PC($\cdot, \cdot$)-Free Berge Graphs

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(n) to find a clique of maximum weight in ...

Coloring square-free Berge graphs

We consider the class of Berge graphs that do not contain a chordless cycle of length four. We present a purely graph-theoretical algorithm that produces an optimal coloring in polynomial time for every graph in that

Even Pairs and Prism Corners in Square-Free Berge Graphs

Let G be a Berge graph such that no induced subgraph is a 4-cycle or a line-graph of a bipartite subdivision of K4. We show that every such graph G either is a complete graph or has an even pair.

Chair-Free Berge Graphs Are Perfect

A graph G is called Berge if neither G nor its complement contains a chordless cycle with an odd number of nodes. The famous Berge’s Strong Perfect Graph Conjecture asserts that every Berge graph is perfect. A chair is a graph with nodes {a, b, c, d, e} and edges {ab, bc, cd, eb}. We prove that a Berge graph with no induced chair (chair-free) is perfect or, equivalently, that the Strong Perfect...

Square-free perfect graphs