Results 301 to 310 of about 9,612,020 (345)

Local antimagic chromatic number of trees - I

Journal of Discrete Mathematical Sciences and Cryptography, 2020
Let G = (V, E) be a connected graph with |V|= n and |E|= m. A bijection f : E → {1, 2, … , m} is called a local antimagic lableing if for any two adjacent vertices u and v, w(u) ≠ w(v), where w(u)= ∑ e ϵE(u) f (e) and E(u) is the set of edges incident to
K. Premalatha, S. Arumugam, Yi-Chun Lee, Tao-Ming Wang   +3 more
semanticscholar   +1 more source

Graphs Whose Circular Chromatic Number Equals the Chromatic Number

Combinatorica, 1999
The circular chromatic number of a graph is the infimum (in fact, the minimum) of \({k}/{d}\) where there is a coloring \(f\) of the vertices with colors \(1,2,\dots,k\) in such a way that \(d\leq | f(x)-f(y)| \leq k-d\) holds when \(x\), \(y\) are adjacent.
openaire   +2 more sources

Chromatic Scheduling and the Chromatic Number Problem

Management Science, 1972
The chromatic scheduling problem may be defined as any problem in which the solution is a partition of a set of objects. Since the partitions may not be distinct, redundant solutions can be generated when partial enumeration techniques are applied to chromatic scheduling problems. The necessary theory is developed to prevent redundant solutions in the
openaire   +1 more source

Chromatic Number

1999
Abstract Erdos and Hajnal (1966) and Lovász (1968, 1968a) were apparently the first to consider (weak) vertex-colourings of hypergraphs. Somewhat later, Berge (1973) formalized the notions of weak and strong chromatic numbers of hypergraphs.
Charles J Colbourn, Alexander Rosa
openaire   +1 more source

Induced Subgraphs of Graphs With Large Chromatic Number. X. Holes of Specific Residue

Combinatorica, 2017
A large body of research in graph theory concerns the induced subgraphs of graphs with large chromatic number, and especially which induced cycles must occur.
A. Scott, P. Seymour
semanticscholar   +1 more source

The Chromatic Number of the Plane is At Least 5: A New Proof

Discrete & Computational Geometry, 2018
We present an alternate proof of the fact that given any 4-coloring of the plane there exist two points one unit apart which are identically colored.
G. Exoo, D. Ismailescu
semanticscholar   +1 more source

Star chromatic number

Journal of Graph Theory, 1988
AbstractA generalization of the chromatic number of a graph is introduced such that the colors are integers modulo n, and the colors on adjacent vertices are required to be as far apart as possible.
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Edge‐face chromatic number and edge chromatic number of simple plane graphs

Journal of Graph Theory, 2005
AbstractGiven a simple plane graph G, an edge‐face k‐coloring of G is a function ϕ : E(G) ∪ F(G) →  {1,…,k} such that, for any two adjacent or incident elements a, b ∈ E(G) ∪ F(G), ϕ(a) ≠ ϕ(b). Let χe(G), χef(G), and Δ(G) denote the edge chromatic number, the edge‐face chromatic number, and the maximum degree of G, respectively. In this paper, we prove
Luo, Rong, Zhang, Cun-Quan
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Eigenvalues and chromatic number of a signed graph

, 2021
Wen Wang, Zhidan Yan, Jianguo Qian
semanticscholar   +1 more source

On the Strong Chromatic Number

Combinatorics, Probability and Computing, 2004
The author proves that for every finite graph \(G\) the strong chromatic number of \(G\) is at most \(3\Delta(G)-1\), where \(\Delta(G)\) is the maximum vertex degree of \(G\).
openaire   +2 more sources