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An Optimal Algorithm for Finding Frieze–Kannan Regular Partitions

Published online by Cambridge University Press:  23 April 2014

DOMINGOS DELLAMONICA Jr ,
SUBRAHMANYAM KALYANASUNDARAM ,
DANIEL M. MARTIN ,
VOJTĚCH RÖDL  and
ASAF SHAPIRA
DOMINGOS DELLAMONICA Jr
Affiliation:
Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA (e-mail: ddellam@mathcs.emory.edu)
SUBRAHMANYAM KALYANASUNDARAM
Affiliation:
Department of Computer Science and Engineering, IIT Hyderabad, India (e-mail: subruk@iith.ac.in)
DANIEL M. MARTIN
Affiliation:
Center for Mathematics, Computer Science and Cognition, Universidade Federal do ABC, Santo André, SP 09210-170Brazil (e-mail: daniel.martin@ufabc.edu.br)
VOJTĚCH RÖDL
Affiliation:
Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA (e-mail: rodl@mathcs.emory.edu)
ASAF SHAPIRA
Affiliation:
School of Mathematics, Tel Aviv University, Tel Aviv, Israel69978 (e-mail: asafico@tau.ac.il)
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Abstract

In this paper we prove that two local conditions involving the degrees and co-degrees in a graph can be used to determine whether a given vertex partition is Frieze–Kannan regular. With a more refined version of these two local conditions we provide a deterministic algorithm that obtains a Frieze–Kannan regular partition of any graph G in time O(|V(G)|2).

Keywords

Primary 05C35Secondary 05C4205C50
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 24 , Issue 2 , March 2015 , pp. 407 - 437
Copyright
Copyright © Cambridge University Press 2014 

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