Stable mixed graphs

Stable Mixed Graphs

In this paper we study classes of graphs with three types of edges that capture the modified independence structure of a directed acyclic graph (DAG) after marginalisation over unobserved variables and conditioning on selection variables using the m-separation criterion. These include MC, summary, and ancestral graphs. As a modification of MC graphs we define the class of ribbonless graphs (RGs...

Stable Equimatchable Graphs

A graph G is equimatchable if every maximal matching of G has the same cardinality. We are interested in equimatchable graphs such that the removal of any edge from the graph preserves the equimatchability. We call an equimatchable graph G edge-stable if G\e is equimatchable for any e ∈ E(G). After noticing that edge-stable equimatchable graphs are either 2-connected factor-critical or bipartit...

Stable properties of graphs

143 Hasratian, A.S. and N.K. Khachatrian, Stable properties of graphs, Discrete Mathematics 90 (1991) 143-152. For many properties P Bondy and Chvatal (1976) have found sufficient conditions such that if a graph G + uv has property P then G itself has property P. In this paper we will give a generalization that will improve ten of these conditions.

Extremal Stable Graphs

Extremal P4-stable graphs

Call a graph G k-stable (with respect to some graph H) if, deleting any k edges of G, the remaining graph still contains H as a subgraph. For a fixed H, the minimum number of edges in a k-stable graph is denoted by S(k). We prove general bounds on S(k) and compute the exact value of the function S(k) for H = P4. The main result can be applied to extremal k-edge-hamiltonian hypergraphs.