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  • 3-facial edge-coloring of plane graphs
    Hornák, Mirko ; Lužar, Borut ; Štorgel, Kenny
    An ▫$\ell$▫-facial edge-coloring of a plane graph is a coloring of its edges such that any two edges at distance at most ▫$\ell$▫ on a boundary walk of any face receive distinct colors. It is the ... edge-coloring variant of the ▫$\ell$▫-facial vertex coloring, which arose as a generalization of the well-known cyclic coloring. It is conjectured that at most ▫$3\ell + 1$▫ colors suffice for an ▫$\ell$▫-facial edge-coloring of any plane graph. The conjecture has only been confirmed for ▫$\ell \le 2$▫, and in this paper, we prove its validity for ▫$\ell = 3$▫.
    Vir: Discrete mathematics. - ISSN 0012-365X (iss. 5, Vol. 346, 2023, str. 1-16)
    Vrsta gradiva - članek, sestavni del
    Leto - 2023
    Jezik - angleški
    COBISS.SI-ID - 143268867
    DOI

vir: Discrete mathematics. - ISSN 0012-365X (iss. 5, Vol. 346, 2023, str. 1-16)

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