Planar graphs without 4-cycles and close triangles are (2, 0, 0)-colorable

Heather Hoskins, Runrun Liu, Jennifer Vandenbussche () and Gexin Yu ()
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Heather Hoskins: The College of William and Mary
Runrun Liu: Central China Normal University
Jennifer Vandenbussche: Kennesaw State University
Gexin Yu: The College of William and Mary

Journal of Combinatorial Optimization, 2018, vol. 36, issue 2, No 2, 346-364

Abstract: Abstract For a set of nonnegative integers $$c_1, \ldots , c_k$$ c 1 , … , c k , a $$(c_1, c_2,\ldots , c_k)$$ ( c 1 , c 2 , … , c k ) -coloring of a graph G is a partition of V(G) into $$V_1, \ldots , V_k$$ V 1 , … , V k such that for every i, $$1\le i\le k, G[V_i]$$ 1 ≤ i ≤ k , G [ V i ] has maximum degree at most $$c_i$$ c i . We prove that all planar graphs without 4-cycles and no less than two edges between triangles are (2, 0, 0)-colorable.

Keywords: Planar graphs; 3-Colorable; Discharging (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-018-0298-2

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