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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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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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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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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 Optimal Beyond-Planar Graphs
Computing in Geometry and Topology, 2023 A graph is beyond-planar if it can be drawn in the plane with a specific restriction on crossings. Several types of beyond-planar graphs have been investigated, such as k-planar graphs where every edge is crossed at most k times and RAC graphs where ...
Franz Brandenburg
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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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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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Fast separation in a graph with an excluded minor [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Let $G$ be an $n$-vertex $m$-edge graph with weighted vertices. A pair of vertex sets $A,B \subseteq V(G)$ is a $\frac{2}{3} - \textit{separation}$ of $\textit{order}$ $|A \cap B|$ if $A \cup B = V(G)$, there is no edge between $A \backslash B$ and $B ...
Bruce Reed, David R. Wood
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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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