Algorithms for Square-3PC(., .)-Free Berge Graphs
نویسندگان
چکیده
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 such a graph. We also consider several subgraph-detection problems related to this class. AMS classification: 68R10, 68Q25, 05C85, 05C17, 90C27.
منابع مشابه
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
متن کاملEven 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.
متن کاملChair-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...
متن کاملRecognizing Dart - Free Perfect Graphs 1317
A graph G is called a Berge graph if neither G nor its complement contains a chordless cycle whose length is odd and at least five; what we call a dart is the graph with vertices u, v, w, x, y and edges uv, vw, uy, vy, wy, xy; a graph is called dart-free if it has no induced subgraph isomorphic to the dart. We present a polynomial-time algorithm to recognize dart-free Berge graphs; this algorit...
متن کاملClaw-free graphs with strongly perfect complements. Fractional and integral version, Part II: Nontrivial strip-structures
Strongly perfect graphs have been studied by several authors (e.g., Berge andDuchet (1984) [1], Ravindra (1984) [7] and Wang (2006) [8]). In a series of two papers, the current paper being the second 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. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Discrete Math.
دوره 22 شماره
صفحات -
تاریخ انتشار 2008