Equitable partition of planar graphs

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An equitable k-partition of a graph G is a collection of induced subgraphs (G[V-1], G[V-2], ... , G[V-k]) of G such that (V-1, V-2, ... , V-k) is a partition of V(G) and -1 <= |V-i| - |V-j| <= 1 for all 1 <= i < j <= k. We prove that every planar graph admits an equitable 2-partition into 3-degenerate graphs, an equitable 3-partition into 2-degenerate graphs, and an equitable 3-partition into two forests and one graph. (c) 2021 Elsevier B.V. All rights reserved.
Publisher
ELSEVIER
Issue Date
2021-06
Language
English
Article Type
Article
Citation

DISCRETE MATHEMATICS, v.344, no.6

ISSN
0012-365X
DOI
10.1016/j.disc.2021.112351
URI
http://hdl.handle.net/10203/285258
Appears in Collection
MA-Journal Papers(저널논문)
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