A graph G is α-critical (or removal-critical) if α(G–e) = α(G)+1 for all edges ∈ 2 E(G), where α( G) is the vertex independence number of G. Similarly, a graph G is contraction-critical if α(G\e ) = α(G) – 1 for all edges e ∈ (G). This document discusses certain properties of removal-critical and contractioncritical graphs, and the enumeration of such graphs (up to 13 vertices and 17 vertices, respectively). It also discusses methods of constructing removal-critical graphs from smaller removal-critical graphs, including vertex duplication, splicing, buckling, and 1-joining. Finally, it discusses the number of removal-critical graphs that can or cannot be produced using these constructions.
|Commitee:||McDonald, Judith J., Tsatsomeros, Michael|
|School:||Washington State University|
|School Location:||United States -- Washington|
|Source:||DAI-B 76/11(E), Dissertation Abstracts International|
|Keywords:||Alpha critical graphs, Removal-critical graphs|
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