Results 21 to 30 of about 6,626,501 (294)
On the Total Set Chromatic Number of Graphs
Theory and Applications of Graphs, 2022 Given a vertex coloring c of a graph, the neighborhood color set of a vertex is defined to be the set of all of its neighbors’ colors. The coloring c is called a set coloring if any two adjacent vertices have different neighborhood color sets.
Mark Anthony C. Tolentino +2 more
doaj +1 more source
On List Equitable Total Colorings of the Generalized Theta Graph
Discussiones Mathematicae Graph Theory, 2021 In 2003, Kostochka, Pelsmajer, and West introduced a list analogue of equitable coloring called equitable choosability. A k-assignment, L, for a graph G assigns a list, L(v), of k available colors to each v ∈ V (G), and an equitable L-coloring of G is a ...
Mudrock Jeffrey A. +2 more
doaj +1 more source
Zig-zag facial total-coloring of plane graphs [PDF]
Opuscula Mathematica, 2018 In this paper we introduce the concept of zig-zag facial total-coloring of plane graphs. We obtain lower and upper bounds for the minimum number of colors which is necessary for such a coloring.
Július Czap +2 more
doaj +1 more source
Neighbor sum distinguishing list total coloring of IC-planar graphs without 5-cycles [PDF]
, 2022 summary:Let $G=(V(G),E(G))$ be a simple graph and $E_{G}(v)$ denote the set of edges incident with a vertex $v$. A neighbor sum distinguishing (NSD) total coloring $\phi $ of $G$ is a proper total coloring of $G$ such that $\sum _{z\in E_{G}(u)\cup \{u\}}
Zhang, Donghan
core +1 more source
Neighbor Distinguishing Colorings of Graphs with the Restriction for Maximum Average Degree
Axioms, 2023 Neighbor distinguishing colorings of graphs represent powerful tools for solving the channel assignment problem in wireless communication networks. They consist of two forms of coloring: neighbor distinguishing edge coloring, and neighbor distinguishing ...
Jingjing Huo +3 more
doaj +1 more source
The benefits of coloring pages for Varityskuvat
, 2022 Coloring makes adults feel like a child again and takes them back to the happiest and most carefree period of their lives. Remembering some of these moments helps us relax and be more optimistic about the future.
Jones Andrew
core +1 more source
Journal of Combinatorial Theory, Series B, 1993 AbstractWe show that as n → ∞ the proportion of graphs on vertices 1, 2, ..., n with total chromatic number χ″ > Δ + 1 is very small; and the proportion with χ″ > Δ + 2 is very very small. Here Δ denotes the maximum vertex degree. We also give an easy new deterministic upper bound on χ″ (proved randomly).
Colin J. H. McDiarmid, Bruce A. Reed
openaire +1 more source
On (p, 1)-Total Labelling of Some 1-Planar Graphs
Discussiones Mathematicae Graph Theory, 2021 A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that the (p, 1)-total labelling number (p ≥ 2) of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that Δ (G) ≥
Niu Bei, Zhang Xin
doaj +1 more source
Coloring count cones of planar graphs [PDF]
, 2022 For a plane near‐triangulation G with the outer face bounded by a cycle C, let nG⋆ denote the function that to each 4‐coloring ψ of C assigns the number of ways ψ extends to a 4‐coloring of G.
Lidicky, Bernard, Dvořák, Zdeněk
core
On a Total Version of 1-2-3 Conjecture
Discussiones Mathematicae Graph Theory, 2020 A total k-coloring of a graph G is a coloring of vertices and edges of G using colors of the set {1, . . . , k}. These colors can be used to distinguish adjacent vertices of G. There are many possibilities of such a distinction.
Baudon Olivier +5 more
doaj +1 more source