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An identifying operation on a 1-planar graph with an application to acyclic coloring

Author

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  • Tan, Qiuyue
  • Qiu, Haizhen
  • Wang, Yiqiao
  • Wang, Kan

Abstract

This paper introduces a graph operation and gives its applications. Given a 1-plane graph M and its crossing point x formed by two crossing edges uu′ and vv′, an Identifying Operation with respect to x is defined in two steps: (1) identifying u and v such that x vanishes; (2) deleting loops and multi-edges (if exists). Using Identifying Operation to every crossing point, we change M into its associated plane graph M⁎. Under some conditions, we show that χa(M)≤2χa(M⁎), where the parameters χa(M) and χa(M⁎) represent the acyclic-chromatic-number of M and M⁎, respectively. This generalizes a result established by Yang et al. in 2018.

Suggested Citation

  • Tan, Qiuyue & Qiu, Haizhen & Wang, Yiqiao & Wang, Kan, 2026. "An identifying operation on a 1-planar graph with an application to acyclic coloring," Applied Mathematics and Computation, Elsevier, vol. 508(C).
    • Handle: RePEc:eee:apmaco:v:508:y:2026:i:c:s0096300325003406
    DOI: 10.1016/j.amc.2025.129614
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