Partially critical indecomposable graphs
DOI:
https://doi.org/10.11575/cdm.v3i2.62003Abstract
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 2 I and x 2 V \ I, {a, x} 2 E if and only if {b, x} 2 E. For example, ;, {x}, where x 2 V , and V are intervals of G called trivial intervals. A graph is indecomposable if all its intervals are trivial; otherwise, it is decomposable. Given an indecomposable graph G = (V,E), consider a proper subset X of V such that |X| 4 and G(X) is indecomposable. The graph G is critical according to G(X) if for every x 2 V \ X, G(V \ {x}) is decomposable. A graph is partially critical if it is critical according to one of its indecomposable subgraphs containing at least 4 vertices. In this paper, we characterize the partially critical graphs.Downloads
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