Sufficient conditions for triangle-free graphs to be optimally restricted edge-connected

Meierling, Dirk; Volkmann, Lutz

doi:10.1016/j.dam.2012.03.020

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Cited by 4 publications

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“…Lemma 2.2 (Corollary 3.2 in [8]). Every connected triangle-free graph of order n with δ(G) ≥ 3 and ξ 3 (G) ≥ n + 1 is λ 3 -optimal.…”

Section: Graph Parametersmentioning

confidence: 98%

Uniform scrambles on graphs

Cenek,

Ferguson,

Gebre

et al. 2021

Preprint

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A scramble on a connected multigraph is a collection of connected subgraphs that generalizes the notion of a bramble. The maximum order of a scramble, called the scramble number of a graph, was recently developed as a tool for lower bounding divisorial gonality. We present results on the scramble of all connected subgraphs with a fixed number of vertices, using these to calculate scramble number and gonality both for large families of graphs, and for specific examples like the 4-and 5-dimensional hypercube graphs. We also study the computational complexity of the egg-cut number of a scramble.

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“…Lemma 2.2 (Corollary 3.2 in [8]). Every connected triangle-free graph of order n with δ(G) ≥ 3 and ξ 3 (G) ≥ n + 1 is λ 3 -optimal.…”

Section: Graph Parametersmentioning

confidence: 98%