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Immersions of Directed Graphs in Tournaments [PDF]
Random Structures &Algorithms, Volume 66, Issue 1, January 2025., 2023 Recently, Draganić, Munhá Correia, Sudakov and Yuster (2022) showed that every tournament on (2+o(1))k2$$ \left(2+o(1)\right){k}^2 $$ vertices contains a 1‐subdivision of a transitive tournament on k$$ k $$ vertices, which is tight up to a constant ...
António Girão, Robert Hancock
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Heroes in oriented complete multipartite graphs [PDF]
Journal of Graph Theory, 2022 The dichromatic number of a digraph is the minimum size of a partition of its vertices into acyclic induced subgraphs. Given a class of digraphs C ${\mathscr{C}}$ , a digraph H $H$ is a hero in C ${\mathscr{C}}$ if H $H$ ‐free digraphs of C ${\mathscr{C}}
Pierre Aboulker +2 more
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Journal of Algebra Combinatorics Discrete Structures and Applications, 2021 A $(0,1)$-labelling of a set is said to be {\em friendly} if approximately one half the elements of the set are labelled 0 and one half labelled 1. Let $g$ be a labelling of the edge set of a graph that is induced by a labelling $f$ of the vertex set. If
LeRoy B. Beasley +3 more
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A Magnetic Framelet-Based Convolutional Neural Network for Directed Graphs [PDF]
IEEE International Conference on Acoustics, Speech, and Signal Processing, 2022 Spectral Graph Convolutional Networks (spectral GCNNs), a powerful tool for analyzing and processing graph data, typically apply frequency filtering via Fourier transform to obtain representations with selective information.
Lequan Lin, Junbin Gao
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Combinatorica, 2019 We prove a conjecture of Fox, Huang, and Lee that characterizes directed graphs that have constant density in all tournaments: they are disjoint unions of trees that are each constructed in a certain recursive way.
Yufei Zhao, Yunkun Zhou
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A Simple Yet Effective SVD-GCN for Directed Graphs [PDF]
arXiv.org, 2022 In this paper, we will present a simple yet effective way for directed Graph (digraph) Convolutional Neural Networks based on the classic Singular Value Decomposition (SVD), named SVD-GCN for digraphs.
Chunya Zou +3 more
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The Diachromatic Number of Digraphs [PDF]
Electronic Journal of Combinatorics, 2017 We consider the extension to directed graphs of the concept of achromatic number in terms of acyclic vertex colorings. The achromatic number have been intensely studied since it was introduced by Harary, Hedetniemi and Prins in 1967.
G. Araujo-Pardo +3 more
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Journal of Graph Theory, 2015 The dichromatic number χ⃗(D) of a digraph D is the least number k such that the vertex set of D can be partitioned into k parts each of which induces an acyclic subdigraph. Introduced by Neumann‐Lara in 1982, this digraph invariant shares many properties
Julien Bensmail +2 more
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Complexity Results for a Cops and Robber Game on Directed Graphs [PDF]
NetworksWe investigate a cops and robber game on directed graphs, where the robber moves along the arcs of the graph, whereas the cops can select any position at each time step.
Walid Ben-Ameur, Alessandro Maddaloni
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Disjoint Cycles of Different Lengths in Graphs and Digraphs [PDF]
Electronic Journal of Combinatorics, 2015 Understanding how the cycles of a graph or digraph behave in general has always been an important point of graph theory. In this paper, we study the question of finding a set of $k$ vertex-disjoint cycles (resp.
Julien Bensmail +4 more
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