3 research outputs found
Graphs whose indecomposability graph is 2-covered
Given a graph , a subset of is an interval of provided
that for any and , if and only
if . For example, , and are
intervals of , called trivial intervals. A graph whose intervals are trivial
is indecomposable; otherwise, it is decomposable. According to Ille, the
indecomposability graph of an undirected indecomposable graph is the graph
whose vertices are those of and edges are the unordered
pairs of distinct vertices such that the induced subgraph is indecomposable. We characterize the indecomposable
graphs whose admits a vertex cover of size 2.Comment: 31 pages, 5 figure