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Distinguishing infinite star-free graphs

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  • Stawiski, Marcin

Abstract

Call a vertex or an edge colouring of a graph distinguishing, if is not preserved by any non-identity automorphism. For a graph H, we say that a graph G is H-free if there is no induced subgraph of G, which is isomorphic to H. Gorzkowska, Kargul, Musiał and Pal proved that for every natural number n greater than 2 each finite connected K1,n-free graph on at least six vertices has a distinguishing edge colouring using at most n−1 colours. We extend this result to all locally finite connected K1,n-free graphs on at least six vertices.

Suggested Citation

  • Stawiski, Marcin, 2025. "Distinguishing infinite star-free graphs," Applied Mathematics and Computation, Elsevier, vol. 495(C).
    • Handle: RePEc:eee:apmaco:v:495:y:2025:i:c:s0096300325000372
    DOI: 10.1016/j.amc.2025.129310
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