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

Author

Listed:
  • 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
    Central China Normal University)

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.

Suggested Citation

  • Heather Hoskins & Runrun Liu & Jennifer Vandenbussche & Gexin Yu, 2018. "Planar graphs without 4-cycles and close triangles are (2, 0, 0)-colorable," Journal of Combinatorial Optimization, Springer, vol. 36(2), pages 346-364, August.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:2:d:10.1007_s10878-018-0298-2
    DOI: 10.1007/s10878-018-0298-2
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    References listed on IDEAS

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    1. Lingji Xu & Zhengke Miao & Yingqian Wang, 2014. "Every planar graph with cycles of length neither 4 nor 5 is $$(1,1,0)$$ -colorable," Journal of Combinatorial Optimization, Springer, vol. 28(4), pages 774-786, November.
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