Algorithms for finding optimal paths in network games with p players

We study the problem of finding optimal paths in network games with p players. Some polynomial-time algorithms for finding optimal paths and optimal by Nash strategies of the players in network games with p players are proposed

Kernelization and Parameterized Algorithms for 3-Path Vertex Cover

A 3-path vertex cover in a graph is a vertex subset $C$ such that every path of three vertices contains at least one vertex from $C$. The parameterized 3-path vertex cover problem asks whether a graph has a 3-path vertex cover of size at most $k$. In this paper, we give a kernel of $5k$ vertices and an $O^*(1.7485^k)$-time and polynomial-space algorithm for this problem, both new results improve previous known bounds.Comment: in TAMC 2016, LNCS 9796, 201

Bounding clique-width via perfect graphs

We continue the study into the clique-width of graph classes defined by two forbidden induced graphs. We present three new classes of bounded clique-width and one of unbounded clique-width. The four new graph classes have in common that one of their two forbidden induced subgraphs is the diamond. To prove boundedness of clique-width for the first three cases we develop a technique based on bounding clique covering number in combination with reduction to subclasses of perfect graphs. We extend our proof of unboundedness for the fourth case to show that Graph Isomorphism is Graph Isomorphism-complete on the same graph class

Clique-width : harnessing the power of atoms.

Many NP-complete graph problems are polynomial-time solvable on graph classes of bounded clique-width. Several of these problems are polynomial-time solvable on a hereditary graph class G if they are so on the atoms (graphs with no clique cut-set) of G . Hence, we initiate a systematic study into boundedness of clique-width of atoms of hereditary graph classes. A graph G is H-free if H is not an induced subgraph of G, and it is (H1,H2) -free if it is both H1 -free and H2 -free. A class of H-free graphs has bounded clique-width if and only if its atoms have this property. This is no longer true for (H1,H2) -free graphs, as evidenced by one known example. We prove the existence of another such pair (H1,H2) and classify the boundedness of clique-width on (H1,H2) -free atoms for all but 18 cases

Independent domination in finitely defined classes of graphs

AbstractWe study the independent dominating set problem restricted to graph classes defined by finitely many forbidden induced subgraphs. The main result is two sufficient conditions for the problem to be NP-hard in a finitely defined class of graphs. We conjecture that those conditions are also necessary and describe several classes of graphs verifying the conjecture

NP-hard graph problems and boundary classes of graphs

Any graph problem, which is NP-hard in general graphs, becomes polynomial-time solvable when restricted to graphs in special classes. When does a difficult problem become easy? To answer this question we study the notion of boundary classes. In the present paper we define this notion in its most general form, describe several approaches to identify boundary classes and apply them to various graph problems