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  • On the lightness of chordal 4-cycle in 1-planar graphs with high minimum degree
    Zhang, Xin, matematik ; Liu, Guizhen, 1944-
    A graph ▫$G$▫ is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. The family of 1-planar graphs with minimum vertex degree at least ▫$\delta$▫ and ... minimum edge degree at least ▫$\varepsilon$▫ is denoted by ▫$\mathcal{P}_\delta^1(\varepsilon)$▫. In this paper, it is proved that every graph in ▫$\mathcal{P}_7^1(14)$▫ (resp. ▫$\mathcal{P}_6^1(13)$▫) contains a copy of chordal 4-cycle with all vertices of degree at most 10 (resp. 12).
    Vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 7, no. 2, 2014, str. 281-291)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2014
    Jezik - angleški
    COBISS.SI-ID - 17046105

vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 7, no. 2, 2014, str. 281-291)

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