Results 41 to 50 of about 3,916 (152)
Palette Sparsification Beyond (Δ+1) Vertex Coloring [PDF]
, 2020 A recent palette sparsification theorem of Assadi, Chen, and Khanna [SODA'19] states that in every n-vertex graph G with maximum degree Δ, sampling O(log n) colors per each vertex independently from Δ+1 colors almost certainly allows for proper coloring ...
Alon, Noga, Assadi, Sepehr
core +1 more source
Polyhedral studies on vertex coloring problems [PDF]
, 2020 Many variants of the vertex coloring problem have been de ned, such as precoloring extension, μ-coloring, (γ ; μ)-coloring, and list coloring. These problems are NP-hard, as they generalize the classical vertex coloring problem.
Marenco, Javier, Delle Donne, Diego
core +2 more sources
Global Dominator Chromatic Number of Certain Graphs [PDF]
Mathematics Interdisciplinary ResearchFor a graph G=(V,E) and a vertex subset $D\subseteq V$, a vertex $v\in V$ is called a dominator of D if v is adjacent to every vertex in D, and an anti-dominator of D if v is not adjacent to any vertex in D. Given a coloring $C=\{V_{1},V_{2},\ldots,
Hadi Nouri Samani +2 more
doaj +1 more source
On the path-avoidance vertex-coloring game [PDF]
Electronic Notes in Discrete Mathematics, 2011 For any graph $F$ and any integer $r\geq 2$, the online vertex-Ramsey density of $F$ and $r$, denoted $m^*(F,r)$, is a parameter defined via a deterministic two-player Ramsey-type game (Painter vs. Builder). This parameter was introduced in a recent paper [arXiv:1103.5849], where it was shown that the online vertex-Ramsey density determines the ...
Mütze, T., Spöhel, R.
openaire +6 more sources
On Irregular Colorings of Unicyclic Graph Family
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023 Irregular coloring is a proper coloring and each vertex on a graph must have a different code. The color code of a vertex v is where and is the number of vertices that are adjacent to v and colored i.
Arika Indah Kristiana +4 more
doaj +1 more source
A Note on Polynomial Algorithm for Cost Coloring of Bipartite Graphs with Δ ≤ 4
Discussiones Mathematicae Graph Theory, 2020 In the note we consider vertex coloring of a graph in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of coloring is the sum of costs incurred at each vertex.
Giaro Krzysztof, Kubale Marek
doaj +1 more source
The Intersection of Two Vertex Coloring Problems [PDF]
Graphs and Combinatorics, 2019 A hole is an induced cycle with at least four vertices. A hole is even if its number of vertices is even. Given a set L of graphs, a graph G is L-free if G does not contain any graph in L as an induced subgraph. Currently, the following two problems are unresolved: the complexity of coloring even hole-free graphs, and the complexity of coloring {4K1 ...
Angèle M. Foley +4 more
openaire +2 more sources
On Twin Edge Colorings of Graphs
Discussiones Mathematicae Graph Theory, 2014 A twin edge k-coloring of a graph G is a proper edge coloring of G with the elements of Zk so that the induced vertex coloring in which the color of a vertex v in G is the sum (in Zk) of the colors of the edges incident with v is a proper vertex coloring.
Andrews Eric +4 more
doaj +1 more source
Upper and lower bounds based on linear programming for the b-coloring problem
EURO Journal on Computational Optimization, 2022 B-coloring is a problem in graph theory. It can model some real applications, as well as being used to enhance solution methods for the classical graph coloring problem. In turn, improved solutions for the classical coloring problem would impact a larger
Roberto Montemanni +2 more
doaj +1 more source
Nonrepetitive vertex colorings of graphs
Discrete Mathematics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jochen Harant, Stanislav Jendrol'
openaire +2 more sources