Results 31 to 40 of about 901,024 (319)

The achromatic number of K_{6} □ K_{7} is 18 [PDF]

Opuscula Mathematica, 2021
A vertex colouring \(f:V(G)\to C\) of a graph \(G\) is complete if for any two distinct colours \(c_1, c_2 \in C\) there is an edge \(\{v_1,v_2\}\in E(G)\) such that \(f(v_i)=c_i\), \(i=1,2\).
Mirko Horňák
doaj   +1 more source

Game Colouring Directed Graphs [PDF]

The Electronic Journal of Combinatorics, 2010
In this paper, a colouring game and two versions of marking games (the weak and the strong) on digraphs are studied. We introduce the weak game chromatic number $\chi_{\rm wg}(D)$ and the weak game colouring number ${\rm wgcol}(D)$ of digraphs $D$. It is proved that if $D$ is an oriented planar graph, then $\chi_{\rm wg}(D)$ $\le {\rm wgcol}(D) \le 9$,
Yang, Daqing, Zhu, Xuding
openaire   +2 more sources

From light edges to strong edge-colouring of 1-planar graphs [PDF]

Discrete Mathematics & Theoretical Computer Science, 2020
A strong edge-colouring of an undirected graph $G$ is an edge-colouring where every two edges at distance at most~$2$ receive distinct colours. The strong chromatic index of $G$ is the least number of colours in a strong edge-colouring of $G$.
Julien Bensmail, François Dross, Hervé Hocquard, Eric Sopena   +3 more
doaj   +1 more source

NP-completeness and One Polynomial Subclass of the Two-Step Graph Colouring Problem

Моделирование и анализ информационных систем, 2019
In this paper, we study the two-step colouring problem for an undirected connected graph. It is required to colour the graph in a given number of colours in a way, when no pair of vertices has the same colour, if these vertices are at a distance of 1 or ...
Natalya Sergeevna Medvedeva, Alexander Valeryevich Smirnov   +1 more
doaj   +1 more source

Generalized List Colouring of Graphs [PDF]

Graphs and Combinatorics, 2021
6 ...
Eun-Kyung Cho, Ilkyoo Choi, Yiting Jiang, Ringi Kim, Boram Park, Jiayan Yan, Xuding Zhu   +6 more
openaire   +2 more sources

Backbone colouring and algorithms for TDMA scheduling [PDF]

Discrete Mathematics & Theoretical Computer Science, 2019
We investigate graph colouring models for the purpose of optimizing TDMA link scheduling in Wireless Networks. Inspired by the BPRN-colouring model recently introduced by Rocha and Sasaki, we introduce a new colouring model, namely the BMRN-colouring ...
Julien Bensmail, Thibaut Blanc, Nathann Cohen, Frédéric Havet, Leonardo Rocha   +4 more
doaj   +1 more source

The Complexity of 3-Colouring H-Colourable Graphs [PDF]

2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS), 2019
To appear in FOCS ...
Krokhin, A., Oprsal, J.
openaire   +3 more sources

Consecutive Colouring of Oriented Graphs [PDF]

Results in Mathematics, 2021
AbstractWe consider arc colourings of oriented graphs such that for each vertex the colours of all out-arcs incident with the vertex and the colours of all in-arcs incident with the vertex form intervals. We prove that the existence of such a colouring is an NP-complete problem.
Marta Borowiecka-Olszewska, Ewa Drgas‐Burchardt, Nahid Yelene Javier-Nol, Rita Zuazua   +3 more
openaire   +1 more source

Cop-width, flip-width and strong colouring numbers [PDF]

Discrete Mathematics & Theoretical Computer Science
Cop-width and flip-width are new families of graph parameters introduced by Toru\'nczyk (2023) that generalise treewidth, degeneracy, generalised colouring numbers, clique-width and twin-width.
Robert Hickingbotham
doaj   +1 more source

Clustered colouring of graph classes with bounded treedepth or pathwidth [PDF]

Combinatorics, probability & computing, 2020
The "clustered chromatic number" of a class of graphs is the minimum integer $k$ such that for some integer $c$ every graph in the class is $k$-colourable with monochromatic components of size at most $c$.
S. Norin, A. Scott, D. Wood
semanticscholar   +1 more source