NDLI: Solving Partition Problems with Colour-Bipartitions

Content Provider	Springer Nature Link
Author	Huang, Jing Churchley, Ross
Copyright Year	2012
Abstract	Polar, monopolar, and unipolar graphs are defined in terms of the existence of certain vertex partitions. Although it is polynomial to determine whether a graph is unipolar and to find whenever possible a unipolar partition, the problems of recognizing polar and monopolar graphs are both NP-complete in general. These problems have recently been studied for chordal, claw-free, and permutation graphs. Polynomial time algorithms have been found for solving the problems for these classes of graphs, with one exception: polarity recognition remains NP-complete in claw-free graphs. In this paper, we connect these problems to edge-coloured homomorphism problems. We show that finding unipolar partitions in general and finding monopolar partitions for certain classes of graphs can be efficiently reduced to a polynomial-time solvable 2-edge-coloured homomorphism problem, which we call the colour-bipartition problem. This approach unifies the currently known results on monopolarity and extends them to new classes of graphs.
Ending Page	364
Page Count	12
Starting Page	353
File Format	PDF
ISSN	09110119
e-ISSN	14355914
Journal	Graphs and Combinatorics
Issue Number	2
Volume Number	30
Language	English
Publisher	Springer Japan
Publisher Date	2012-11-28
Publisher Place	Tokyo
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Unipolar graphs Factorization, matching, partitioning, covering and packing Partition problems Monopolar graphs Graph algorithms Engineering Design Polynomial algorithm Combinatorics Edge-coloured graphs
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Theoretical Computer Science

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