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  • Induced cycles in triangle graphs
    Lakshmanan, Aparna Savithri ; Bujtás, Csilla ; Tuza, Zsolt
    The triangle graph of a graph ▫$G$▫, denoted by ▫$\mathcal{T}(G)$▫, is the graph whose vertices represent the triangles (▫$K_3$▫ subgraphs) of ▫$G$▫, and two vertices of ▫$\mathcal{T}(G)$▫ are ... adjacent if and only if the corresponding triangles share an edge. In this paper, we characterize graphs whose triangle graph is a cycle and then extend the result to obtain a characterization of ▫$C_n$▫-free triangle graphs. As a consequence, we give a forbidden subgraph characterization of graph ▫$G$▫ for which ▫$\mathcal{T}(G)$▫ is a tree, a chordal graph, or a perfect graph. For the class of graphs whose triangle graph is perfect, we verify a conjecture of the third author concerning packing and covering of triangles.
    Vir: Discrete applied mathematics. - ISSN 0166-218X (Vol. 209, Aug. 2016, str. 264-275)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2016
    Jezik - angleški
    COBISS.SI-ID - 18890585

    Povezava(-e):

    https://doi.org/10.1016/j.dam.2015.12.012
    DOI

vir: Discrete applied mathematics. - ISSN 0166-218X (Vol. 209, Aug. 2016, str. 264-275)

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