Random subgraphs of Cayley graphs over P-groups
In this paper the author studies the largest component of random induced subgraphs of Cayley graphs X{sub n} over a certain class of p-groups P{sub n}. Here P{sub n} consists of p-groups, G{sub n}, that have the properties: (i) G{sub n}/{Phi}(G{sub n}) {congruent} F{sub p}{sup n}, where {Phi}(G{sub n}) is the Frattini subgroup and (ii) {vert_bar}G{sub n}{vert_bar} {le}n{sup Kn}, K > 0. The author then takes minimal Cayley graphs X{sub n} = {Gamma}(G{sub n},S{prime}{sub n}), where S{prime}{sub n} = S{sub n} {union} S{sub n}{sup {minus}1}, and S{sub n} is a minimal G{sub n}-generating set. The random induced subgraphs, {Gamma}{sub n} of X{sub n} are produced by selecting G{sub n}-elements with independent probability {lambda}{sub n}. The subject of this paper is the analysis of the largest component of random induced subgraphs {Gamma}{sub n} < X{sub n}. The author`s main result is, that there exists a positive constant c > 0 such that for {lambda}{sub n} = c ln ({vert_bar}S{prime}{sub n}{vert_bar})/{vert_bar}S{prime}{sub n}{vert_bar} the largest component of random subgraphs of X{sub n} contains almost all vertices.
- Research Organization:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 522717
- Report Number(s):
- LA-UR-97-1913; CONF-9705152-1; ON: DE97008151; TRN: 97:005048
- Resource Relation:
- Conference: European journal of combinatories, Paris (France), 28 May 1997; Other Information: PBD: 1997
- Country of Publication:
- United States
- Language:
- English
Similar Records
Distances in Random Induced Subgraphs of Generalized n-Cubes
Approximate and exact algorithms for the maximum planar subgraph problem