NDLI: Near-proper vertex 2-colorings of sparse graphs

Content Provider	Springer Nature Link
Author	Borodin, O. V. Ivava, A. O.
Copyright Year	2010
Abstract	A graph G is (2, 1)-colorable if its vertices can be partitioned into subsets V $_{1}$ and V $_{2}$ such that each component in G[V $_{1}$] contains at most two vertices while G[V $_{2}$] is edgeless. We prove that every graph with maximum average degree mad(G) < 7/3 is (2, 1)-colorable. It follows that every planar graph with girth at least 14 is (2, 1)-colorable. We also construct a planar graph G $_{n}$ with mad (G $_{n}$) = (18n − 2)/(7n − 1) that is not (2, 1)-colorable.
Starting Page	21
Ending Page	23
Page Count	3
File Format	PDF
ISSN	19904789
Journal	Journal of Applied and Industrial Mathematics
Volume Number	4
Issue Number	1
e-ISSN	19904797
Language	English
Publisher	SP MAIK Nauka/Interperiodica
Publisher Date	2010-03-25
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	planar graph girth coloring partition Mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Industrial and Manufacturing Engineering

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Near-proper vertex 2-colorings of sparse graphs