Dominating sets for split and bipartite graphs
Information Processing Letters
About recognizing (&agr; &bgr;) classes of polar graphs
Discrete Mathematics
Partitioning permutations into increasing and decreasing subsequences
Journal of Combinatorial Theory Series A
Generalized split graphs and Ramsey numbers
Journal of Combinatorial Theory Series A
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A finite basis characterization of α-split colorings
Discrete Mathematics - Kleitman and combinatorics: a celebration
r-Bounded k-complete bipartite bihypergraphs and generalized split graphs
Discrete Mathematics
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Independent domination in hereditary classes
Theoretical Computer Science
NP-hard graph problems and boundary classes of graphs
Theoretical Computer Science
Note: On the inapproximability of independent domination in 2P3-free perfect graphs
Theoretical Computer Science
Maximum regular induced subgraphs in 2P3-free graphs
Theoretical Computer Science
| Hi-index | 5.23 |
A graph G is called a satgraph if there exists a partition A ∪ B = V(G) such that • A induces a clique [possibly, A = 0], • B induces a matching [i.e., G(B) is a 1-regular subgraph, possibly, B = 0], and • there are no triangles (a, b, b'), where a ∈ A and b, b' ∈ B.We also introduce the hereditary closure of IAJ, denoted by HIAJ [hereditary satgraphs]. The class HIAJ contains split graphs. In turn, HIAJ is contained in the class of all (1, 2)-split graphs [A. Gyárfás, Generalized split graphs and Ramsey numbers, J. Combin. Theory Ser. A 81 (2) (1998) 255-261], the latter being still not characterized. We characterize satgraphs in terms of forbidden induced subgraphs.There exist close connections between satgraphs and the satisfiability problem [SAT]. In fact, SAT is linear-time equivalent to finding the independent domination number in the corresponding satgraph. It follows that the independent domination problem is NP-complete for the hereditary satgraphs. In particular, it is NP-complete for perfect graphs.