Critically indecomposable graphs

Partially critical indecomposable graphs

Given a graph G = (V, E), with each subset X of V is associated the subgraph G(X) of G induced by X. A subset I of V is an interval of G provided that for any a, b ∈ I and x ∈ V \ I , {a, x} ∈ E if and only if {b, x} ∈ E. For example, ∅, {x}, where x ∈ V , and V are intervals of G called trivial intervals. A graph is indecomposable if all its intervals are trivial; otherwise, it is decomposable...

Minimal indecomposable graphs

Let G=(V,E) be a graph, a subset X of V is an interval of G whenever for a, b E X and xE V X , (a,x)EE (resp. (x,a)EE) if and only if (b,x)EE (resp. (x,b)EE). For instance, 0, {x}, where x E V, and V are intervals of G, called trivial intervals. A graph G is then said to be indecomposable when all of its intervals are trivial. In the opposite case, we will say that G is decomposable. We now int...

Critically indecomposable partially ordered sets, graphs, tournaments and other binary relational structures

A hnite. indecomposabic partially ordered set is said to be critically indecomposahlc if. whenever an clement is removed. the resulting induced partially ordered set is not indccomposabic. The same terminology can be applied to graphs. tournaments, or any other relational structure whose relations are binary and irrcflexive. It will be shown in this paper that critically indecomposable partiall...

Indecomposable Graphs and Signed Domination Numbers

Indecomposable r-graphs and some other counterexamples