Results 1 to 10 of about 168,763 (311)
Complete graph minors and the graph minor structure theorem
Journal of Combinatorial Theory Series B, 2013 The graph minor structure theorem by Robertson and Seymour shows that every graph that excludes a fixed minor can be constructed by a combination of four ingredients: graphs embedded in a surface of bounded genus, a bounded number of vortices of bounded width, a bounded number of apex vertices, and the clique-sum operation.
Gwenael Joret, David R Wood
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Minor-Universal Graph for Graphs on Surfaces
CoRR, 2023 We show that, for every n and every surface $Σ$, there is a graph U embeddable on $Σ$ with at most cn^2 vertices that contains as minor every graph embeddable on $Σ$ with n vertices. The constant c depends polynomially on the Euler genus of $Σ$. This generalizes a well-known result for planar graphs due to Robertson, Seymour, and Thomas [Quickly ...
Cyril Gavoille, Claire Hilaire
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Enhancing the Distinguishability of Minor Fluctuations in Time Series Classification Using Graph Representation: The MFSI-TSC Framework [PDF]
SensorsIn industrial systems, sensors often classify collected time series data for incipient fault diagnosis. However, time series data from sensors during the initial stages of a fault often exhibits minor fluctuation characteristics.
He Nai, Chunlei Zhang, Xianjun Hu
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Edge-group choosability of outerplanar and near-outerplanar graphs [PDF]
Transactions on Combinatorics, 2020 Let $\chi_{gl}(G)$ be the {\it{group choice number}} of $G$. A graph $G$ is called {\it{edge-$k$-group choosable}} if its line graph is $k$-group choosable. The {\it{group-choice index}} of $G$, $\chi'_{gl}(G)$, is the smallest $k$ such that $G$ is edge-$
Amir Khamseh
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Separating layered treewidth and row treewidth [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 Layered treewidth and row treewidth are recently introduced graph parameters that have been key ingredients in the solution of several well-known open problems.
Prosenjit Bose +4 more
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Minor-monotone crossing number [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 The minor crossing number of a graph $G$, $rmmcr(G)$, is defined as the minimum crossing number of all graphs that contain $G$ as a minor. We present some basic properties of this new minor-monotone graph invariant.
Drago Bokal +2 more
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Internally 4-Connected Graphs With No {Cube, V8}-Minor
Discussiones Mathematicae Graph Theory, 2021 A simple graph is a minor of another if the first is obtained from the second by deleting vertices, deleting edges, contracting edges, and deleting loops and parallel edges that are created when we contract edges.
Lewchalermvongs Chanun +1 more
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On Nowhere Zero 4-Flows in Regular Matroids
Theory and Applications of Graphs, 2023 Walton and Welsh proved that if a co-loopless regular matroid M does not have a minor in {M(K(3,3)),M∗(K5)}, then M admits a nowhere zero 4-flow. Lai, Li and Poon proved that if M does not have a minor in {M(K5),M∗(K5)}, then M admits a nowhere zero 4 ...
Xiaofeng Wang, Taoye Zhang, Ju Zhou
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Upper bounds on the non- 3-colourability threshold of random graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2002 We present a full analysis of the expected number of `rigid' 3-colourings of a sparse random graph. This shows that, if the average degree is at least 4.99, then as n → ∞ the expected number of such colourings tends to 0 and so the probability that
Nikolaos Fountoulakis, Colin McDiarmid
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Hitting minors, subdivisions, and immersions in tournaments [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 The Erd\H{o}s-P\'osa property relates parameters of covering and packing of combinatorial structures and has been mostly studied in the setting of undirected graphs.
Jean-Florent Raymond
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