English

Adjective

dismantlable ‎(not comparable)

1. Capable of being dismantled, or taken apart.
2. (set theory) The property of an ordered set such that its elements can listed in an order such that, for every element, the element is irreducible (has exactly one upper or lower cover) in the subset consisting of that element and all subsequent elements.
3. (graph theory) The property of a graph such that its vertices can be listed in an order such that, for every vertex, the vertex is a subdominant vertex (has an adjacent vertex that is adjacent to every other vertex that it is adjacent to) in the induced subgraph generated by that vertex and all subsequent vertices.
   • 2015, Michal Adamaszek, “A note on independence complexes of chordal graphs and dismantling”, in arXiv:

     We show that the independence complex of a chordal graph is contractible if and only if this complex is dismantlable (strong collapsible) and it is homotopy equivalent to a sphere if and only if its core is a cross-polytopal sphere.

References

• Information System on Graph Classes and their Inclusions

Related terms

• dismantlability

Translations