Online graph exploration on a restricted graph class: Optimal solutions for tadpole graphs

The Online Graph Exploration Problem on Restricted Graphs

Harsanyi power solutions for graph-restricted games

We consider cooperative transferable utility games, or simply TU-games, with limited communication structure in which players can cooperate if and only if they are connected in the communication graph. Solutions for such graph games can be obtained by applying standard solutions to a modified or restricted game that takes account of the cooperation restrictions. We discuss Harsanyi solutions wh...

On Graph Isomorphism for Restricted Graph Classes

Graph isomorphism (GI) is one of the few remaining problems in NP whose complexity status couldn’t be solved by classifying it as being either NP-complete or solvable in P. Nevertheless, efficient (polynomial-time or even NC) algorithms for restricted versions of GI have been found over the last four decades. Depending on the graph class, the design and analysis of algorithms for GI use tools f...

Online Graph Exploration with Advice

We study the problem of exploring an unknown undirected graph with non-negative edge weights. Starting at a distinguished initial vertex s, an agent must visit every vertex of the graph and return to s. Upon visiting a node, the agent learns all incident edges, their weights and endpoints. The goal is to find a tour with minimal cost of traversed edges. This variant of the exploration problem h...

Characteristics of Common Neighborhood Graph under Graph Operations and on Cayley Graphs

Let G(V;E) be a graph. The common neighborhood graph (congraph) of G is a graph with vertex set V , in which two vertices are adjacent if and only if they have a common neighbor in G. In this paper, we obtain characteristics of congraphs under graph operations; Graph :::::union:::::, Graph cartesian product, Graph tensor product, and Graph join, and relations between Cayley graphs and its c...