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Acyclic improper choosability of subcubic graphs

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  • Chen, Min
  • Raspaud, André

Abstract

A d-improper k-coloring of a graph G is a mapping φ:V(G)→{1,2,…,k} such that for every color i, the subgraph induced by the vertices of color i has maximum degree d. That is, every vertex can be adjacent to at most d vertices with being the same color as itself. Such a d-improper k-coloring is further said to be acyclic if for every pair of distinct colors, say i and j, the induced subgraph by the edges whose endpoints are colored with i and j is a forest. Meanwhile, we say that G is acyclically (k, d)*-colorable.

Suggested Citation

  • Chen, Min & Raspaud, André, 2019. "Acyclic improper choosability of subcubic graphs," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 92-98.
    • Handle: RePEc:eee:apmaco:v:356:y:2019:i:c:p:92-98
    DOI: 10.1016/j.amc.2019.03.027
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    Cited by:

    1. Wang, Yang & Huang, Danjun & Finbow, Stephen, 2020. "On the vertex partition of planar graphs into forests with bounded degree," Applied Mathematics and Computation, Elsevier, vol. 374(C).

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