Abstract
Let X be a subset of vertices of an undirected graph G = (V, E). G is X-critical if it is indecomposable and its induced subgraph on X vertices is also indecomposable, but all induced subgraphs on V - {w} are decomposable for all w ∈ V - X. We present two results in this paper. The first result states that if G is X-critical, then for every w ∈ V - {x}, G[V -{w}] has a unique non-trivial module and its cardinality is either 2 or |V| - 2. The second result is that the vertices of V - X can be paired up as (a1, b1), . . . , (ak, bk) such that induced subgraphs on subset V - {aj1, bj1, . . . , ajs, bjs} are also X-critical for any collection of pairs {(a j1, bj1), . . . ,(ajs, bjs)}.
Original language | English (US) |
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Pages (from-to) | 690-700 |
Number of pages | 11 |
Journal | Lecture Notes in Computer Science |
Volume | 3595 |
DOIs | |
State | Published - 2005 |
Event | 11th Annual International Conference on Computing and Combinatorics, COCOON 2005 - Kunming, China Duration: Aug 16 2005 → Aug 29 2005 |
ASJC Scopus subject areas
- Theoretical Computer Science
- General Computer Science