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Vertex-minors of graphs: A survey
Discrete Applied MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Donggyu Kim, Sang-il Oum
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Minors in graphs of large girth
Random Structures & Algorithms, 2003AbstractWe show that for every odd integer g ≥ 5 there exists a constant c such that every graph of minimum degree r and girth at least g contains a minor of minimum degree at least cr(g+1)/4. This is best possible up to the value of the constant c for g = 5, 7, and 11.
Daniela Kühn, Deryk Osthus
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Towards the Graph Minor Theorems for Directed Graphs
2015Two key results of Robertson and Seymour's graph minor theory are:1.a structure theorem stating that all graphs excluding some fixed graph as a minor have a tree decomposition into pieces that are almost embeddable in a fixed surface.2.the k-disjoint paths problem is tractable when $$k$$ is a fixed constant: given a graph $$G$$ and $$k$$ pairs $$s_1 ...
Kawarabayashi, Ken-Ichi +1 more
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On the Hyperbolicity Constant in Graph Minors
Bulletin of the Iranian Mathematical Society, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Walter Carballosa +3 more
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Compact topological minors in graphs
Journal of Graph Theory, 2010Summary: Let \(\varepsilon \) be a real number such that \(0 < \varepsilon < \frac{1}{2}\) and \(t\) a positive integer. Let \(n\) be a sufficiently large positive integer as a function of \(t\) and \(\varepsilon \). We show that every \(n\)-vertex graph with at least \(n^{1+\varepsilon }\) edges contains a subdivision of \(K_{t}\) in which each edge ...
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On fixing edges in graph minors
Graphs and Combinatorics, 1996A characterization of graphs with certain minor-type property is given.
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A characterization of graphs with no octahedron minor
J. Graph Theory, 2013Summary: It is proved that a graph does not contain an octahedron minor if and only if it is constructed from \(\{ K_1, K_2, K_3, K_4\} \cup \{C_{2n-1}^2 : n\geq 3\}\) and five other internally 4-connected graphs by 0-, 1-, 2-, and 3-sums.
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Graph states and the variety of principal minors
Annali Di Matematica Pura Ed Applicata, 2023Vincenzo Galgano, Frédéric Holweck
exaly
Graph Minors. XXII. Irrelevant vertices in linkage problems
Journal of Combinatorial Theory Series B, 2012Paul Seymour
exaly