Discrete Mathematics
A semi-strong perfect graph theorem
Journal of Combinatorial Theory Series B
On the complexity of recognizing perfectly orderable graphs
Discrete Mathematics
Recognizing brittle graphs: remarks on a paper of Hoa`ng and Khouzam
Discrete Applied Mathematics
A tree representation for P4-sparse graphs
Discrete Applied Mathematics
Linear time optimization for P 4-sparse graphs
Discrete Applied Mathematics
A linear-time recognition algorithm for P4-reducible graphs
Theoretical Computer Science
P-Components and the Homogeneous Decomposition of Graphs
SIAM Journal on Discrete Mathematics
P4-laden graphs: a new class of brittle graphs
Information Processing Letters
A fast parallel algorithm to recognize P4-sparse graphs
Discrete Applied Mathematics
On the structure of graphs with few P4s
Discrete Applied Mathematics
Graph classes: a survey
Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
Efficient and practical modular decomposition
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Linear-time modular decomposition and efficient transitive orientation of comparability graphs
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Recognizing the P4-structure of bipartite graphs
Discrete Applied Mathematics
Recognizing the P4-structure of block graphs
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
A New Linear Algorithm for Modular Decomposition
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
Discrete Applied Mathematics
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
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Two graphs G and H with the same vertex set V are P4- isomorphic if every four vertices {a, b, c, d} ⊆ V induce a chordless path (denoted by P4) in G if and only if they induce a P4 in H. We call a graph split-perfect if it is P4-isomorphic to a split graph (i.e. a graph being partitionable into a clique and a stable set). This paper characterizes the new class of split-perfect graphs using the concepts of homogeneous sets and p-connected graphs, and leads to a linear time recognition algorithm for split-perfect graphs, as well as linear time algorithms for classical optimization problems on split-perfect graphs based on the primeval decomposition of graphs. These results considerably extend previous ones on smaller classes such as P4-sparse graphs, P4-lite graphs, P4-laden graphs, and (7,3)-graphs. Moreover, split-perfect graphs form a new subclass of brittle graphs containing the superbrittle graphs for which a new characterization is obtained leading to linear time recognition.