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  • A theorem about the channel assignment problem
    Král', Daniel ; Škrekovski, Riste
    A list channel assignment problem is a triple ▫$(G,L,w)$▫ where ▫$G$▫ is a graph, ▫$L$▫ is a function assigning vertices of ▫$G$▫ lists of integers (colours) and ▫$w$▫ is a function assigning edges ... of ▫$G$▫ positive integers (weights). A colouring ▫$c$▫ of the vertices of ▫$G$▫ is proper if ▫$c(v) \in L(v)$▫ for each vertex ▫$v$▫ and ▫$|c(u)-c(v)| \ge w(uv)$▫ for each edge ▫$uv$▫. A weighted degree ▫${\rm deg}_w(v)$▫ of a vertex ▫$v$▫ is the sum of the weights of the edges incident with ▫$v$▫. If ▫$G$▫ is connected. ▫$|L(v)|>{\rm deg}_w(v)$▫ for at least one ▫$v$▫ and ▫$|L(v)| \ge {\rm deg}_w(v)$▫ for all ▫$v$▫, then a proper colourings always exists. A list channel assignment problem is balanced if ▫$|L(v)|={\rm deg}_w(v)$▫ for all ▫$v$▫. We characterize all balanced list channel assignment problems ▫$(G,L,w)$▫ which admits a proper colouring.
    Vir: Preprint series. - ISSN 1318-4865 (Vol. 40, [št.] 816, 2002, str. 1-17)
    Vrsta gradiva - članek, sestavni del
    Leto - 2002
    Jezik - angleški
    COBISS.SI-ID - 11526745

vir: Preprint series. - ISSN 1318-4865 (Vol. 40, [št.] 816, 2002, str. 1-17)

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