On the structure of (P5, gem)-free graphs

On algorithms for (P5, gem)-free graphs

A graph is (P5,gem)-free, when it does not contain P5 (an induced path with five vertices) or a gem (a graph formed by making an universal vertex adjacent to each of the four vertices of the induced path P4) as an induced subgraph. We present O(n2) time recognition algorithms for chordal gem-free and for (P5,gem)free graphs. Using a characterization of (P5,gem)-free graphs by their prime graphs...

Chordal co-gem-free and (P5, gem)-free graphs have bounded clique-width

Gem- And Co-Gem-Free Graphs Have Bounded Clique-Width

The P4 is the induced path of four vertices. The gem consists of a P4 with an additional universal vertex being completely adjacent to the P4, and the co-gem is its complement graph. Gemand co-gem-free graphs generalize the popular class of cographs (i. e. P4-free graphs). The tree structure and algebraic generation of cographs has been crucial for several concepts of graph decomposition such a...

On variations of P4-sparse graphs

Hoàng defined the P4-sparse graphs as the graphs where every set of five vertices induces at most one P4. These graphs attracted considerable attention in connection with the P4-structure of graphs and the fact that P4-sparse graphs have bounded clique-width. Fouquet and Giakoumakis generalized this class to the nicely structured semi-P4-sparse graphs being the (P5, co-P5, co-chair)-free graphs...

On (P5, diamond)-free graphs

We study the stability number, chromatic number and clique cover of graphs with no induced P5 and diamonds. In particular, we provide a way to obtain all imperfect (P5, diamond)-free graphs by iterated point multiplication or substitution from a /nite collection of small basic graphs. Corollaries of this and other structural properties, among which a result of Bacs1 o and Tuza, are (i) combinat...