VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • The ▫$k$▫-independence number of direct products of graphs and Hedetniemi's conjecture
    Špacapan, Simon
    The ▫$k$▫-independence number of ▫$G$▫, denoted as ▫$\alpha_k(G)$▫, is the size of a largest ▫$k$▫-colorable subgraph of ▫$G$▫. The direct product of graphs ▫$G$▫ and ▫$H$▫, denoted as ▫$G \times ... H$▫, is the graph with vertex set ▫$V(G) \times V(H)$▫, where two vertices ▫$(x_1, y_1)$▫ and ▫$(x_2, y_2)$▫ are adjacent in ▫$G \times H$▫, if ▫$x_1$▫ is adjacent to ▫$x_2$▫ in ▫$G$▫ and ▫$y_1$▫ is adjacent to ▫$y_2$▫ in ▫$H$▫. We conjecture that for any graphs ▫$G$▫ and ▫$H$▫, ▫$$\alpha_k(G \times H) \ge \alpha_k(G)|V(H)| + \alpha_k(H)|V(G)| - \alpha_k(G) \alpha_k(H).$$▫ The conjecture is stronger than Hedetniemi's conjecture. We prove the conjecture for ▫$k = 1, 2$▫ and prove that ▫$\alpha_k(G \times H) \ge \alpha_k(G)|V(H)| + \alpha_k(H)|V(G)| - \alpha_k(G) \alpha_k(H)$▫ holds for any ▫$k$▫.
    Vir: European journal of combinatorics = Journal européen de combinatoire = Europäische Zeitschrift für Kombinatorik. - ISSN 0195-6698 (Vol. 32, no. 8, 2011, str. 1377-1383)
    Vrsta gradiva - članek, sestavni del
    Leto - 2011
    Jezik - angleški
    COBISS.SI-ID - 16079705

    Povezava(-e):

    http://dx.doi.org/10.1016/j.ejc.2011.07.002
    Digitalna knjižnica Univerze v Mariboru – DKUM

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