Bounds on the max and min bisection of random cubic and 4-regular graphs

In this paper we present simple randomized algorithms to bisect cubic and 4-regular graphs. These algorithms produce bisections of size asymptotically at most 0.17404n for typical random cubic n-vertex graphs, and n/3+eps n for random 4-regular (any eps>0). We also obtain asymptotic lower bounds...

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Detalles Bibliográficos
Autores: Díaz Cort, Josep|||0000-0003-4422-0067, Do, Norman, Serna Iglesias, María José|||0000-0001-9729-8648, Wormald, Nick
Tipo de recurso: informe técnico
Fecha de publicación:2002
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/97396
Acceso en línea:https://hdl.handle.net/2117/97396
Access Level:acceso abierto
Palabra clave:Random cubic bisection
4-regular graphs bisection
Àrees temàtiques de la UPC::Informàtica::Programació
Descripción
Sumario:In this paper we present simple randomized algorithms to bisect cubic and 4-regular graphs. These algorithms produce bisections of size asymptotically at most 0.17404n for typical random cubic n-vertex graphs, and n/3+eps n for random 4-regular (any eps>0). We also obtain asymptotic lower bounds for the size of the maximum bisection, for random cubic and random 4-regular graphs with $ vertices, of 1.32697 n and 5n/3+eps n, respectively. In all cases except the minimum bisection of cubic graphs, these give new results on the existence of regular graphs with small or large bisections. The randomized algorithms are derived from a greedy algorithm and the analysis is based on the differential equation method.