Relevant bibliographies by topics / Dicritical digraphs

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Academic literature on the topic 'Dicritical digraphs'

Author: Grafiati
Published: 7 July 2024
Last updated: 31 July 2025

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Journal articles on the topic "Dicritical digraphs"

1

Picasarri-Arrieta, Lucas, and Clément Rambaud. "Subdivisions in dicritical digraphs with large order or digirth." European Journal of Combinatorics 122 (December 2024): 104022. http://dx.doi.org/10.1016/j.ejc.2024.104022.

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2

Havet, Frédéric, Florian Hörsch, and Lucas Picasarri-Arrieta. "The 3-Dicritical Semi-Complete Digraphs." Electronic Journal of Combinatorics 32, no. 1 (2025). https://doi.org/10.37236/12820.

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A digraph is $3$-dicritical if it cannot be vertex-partitioned into two sets inducing acyclic digraphs, but each of its proper subdigraphs can. We give a human-readable proof that the collection of 3-dicritical semi-complete digraphs is finite. Further, we give a computer-assisted proof of a full characterization of 3-dicritical semi complete digraphs. There are eight such digraphs, two of which are tournaments. We finally give a general upper bound on the maximum number of arcs in a $3$-dicritical digraph.
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3

Aboulker, Pierre, and Quentin Vermande. "Various Bounds on the Minimum Number of Arcs in a $k$-Dicritical Digraph." Electronic Journal of Combinatorics 31, no. 1 (2024). http://dx.doi.org/10.37236/11549.

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The dichromatic number $\vec{\chi}(G)$ of a digraph $G$ is the least integer $k$ such that $G$ can be partitioned into $k$ acyclic digraphs. A digraph is $k$-dicritical if $\vec{\chi}(G) = k$ and each proper subgraph $H$ of $G$ satisfies $\vec{\chi}(H) \leq k-1$. 
 We prove various bounds on the minimum number of arcs in a $k$-dicritical digraph, a structural result on $k$-dicritical digraphs and a result on list-dicolouring. We characterise $3$-dicritical digraphs $G$ with $(k-1)|V(G)| + 1$ arcs. For $k \geq 4$, we characterise $k$-dicritical digraphs $G$ on at least $k+1$ vertices and w
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4

Havet, Frédéric, Lucas Picasarri‐Arrieta, and Clément Rambaud. "On the minimum number of arcs in 4‐dicritical oriented graphs." Journal of Graph Theory, July 29, 2024. http://dx.doi.org/10.1002/jgt.23159.

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AbstractThe dichromatic number of a digraph is the minimum number of colours needed to colour the vertices of a digraph such that each colour class induces an acyclic subdigraph. A digraph is ‐dicritical if and each proper subdigraph of satisfies . For integers and , we define (resp., ) as the minimum number of arcs possible in a ‐dicritical digraph (resp., oriented graph). Kostochka and Stiebitz have shown that . They also conjectured that there is a constant such that for and large enough. This conjecture is known to be true for . In this work, we prove that every 4‐dicritical oriented graph
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Dissertations / Theses on the topic "Dicritical digraphs"

1

Picasarri-Arrieta, Lucas. "Coloration de graphes dirigés." Electronic Thesis or Diss., Université Côte d'Azur, 2024. http://www.theses.fr/2024COAZ4023.

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Cette thèse est dédiée à l'étude de la dicoloration, une notion de coloration pour les digraphes introduite par ErdH{o}s et Neumann-Lara à la fin des années 1970, ainsi que le paramètre qui lui est associé, à savoir le nombre dichromatique. Au cours des dernières décennies, ces deux notions ont permis de généraliser de nombreux résultats classiques de coloration de graphes. Nous commençons par donner différentes bornes sur le nombre dichromatique des digraphes dont le graphe sous-jacent est un graphe cordal. Ensuite, nous améliorons la borne donnée par le théorème de Brooks pour les digraphes
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