Partitioning Perfect Graphs into Stars

Star Partitions of Perfect Graphs

The partition of graphs into nice subgraphs is a central algorithmic problem with strong ties to matching theory. We study the partitioning of undirected graphs into stars, a problem known to be NP-complete even for the case of stars on three vertices. We perform a thorough computational complexity study of the problem on subclasses of perfect graphs and identify several polynomial-time solvabl...

Haplotype Block Partitioning and tagSNP Selection under the Perfect Phylogeny Model

Single Nucleotide Polymorphisms (SNPs) are the most usual form of polymorphism in human genome.Analyses of genetic variations have revealed that individual genomes share common SNP-haplotypes. Theparticular pattern of these common variations forms a block-like structure on human genome. In this work,we develop a new method based on the Perfect Phylogeny Model to identify haplo...

Perfect Matchings in Edge-Transitive Graphs

We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...

$n$-Array Jacobson graphs

We generalize the notion of Jacobson graphs into $n$-array columns called $n$-array Jacobson graphs and determine their connectivities and diameters. Also, we will study forbidden structures of these graphs and determine when an $n$-array Jacobson graph is planar, outer planar, projective, perfect or domination perfect.

About the Strong Perfect Graph Conjecture on circular partitionable graphs