Results 41 to 50 of about 20,911 (165)
Chromatic numbers of spheres [PDF]
Discrete Mathematics, 2018 The chromatic number of a subset of Euclidean space is the minimal number of colors sufficient for coloring all points of this subset in such a way that any two points at the distance 1 have different colors. We give new upper bounds for chromatic numbers of spheres.
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On the Strong Chromatic Number of Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2006 The strong chromatic number, $χ_S(G)$, of an $n$-vertex graph $G$ is the smallest number $k$ such that after adding $k\lceil n/k\rceil-n$ isolated vertices to $G$ and considering {\bf any} partition of the vertices of the resulting graph into disjoint subsets $V_1, \ldots, V_{\lceil n/k\rceil}$ of size $k$ each, one can find a proper $k$-vertex ...
Maria Axenovich, Ryan R. Martin
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The Locating-Chromatic Number of Origami Graphs
Algorithms, 2021 The locating-chromatic number of a graph combines two graph concepts, namely coloring vertices and partition dimension of a graph. The locating-chromatic number is the smallest k such that G has a locating k-coloring, denoted by χL(G).
Agus Irawan +3 more
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The Chromatic Number of a Signed Graph [PDF]
The Electronic Journal of Combinatorics, 2016 In 1982, Zaslavsky introduced the concept of a proper vertex colouring of a signed graph $G$ as a mapping $\phi\colon V(G)\to \mathbb{Z}$ such that for any two adjacent vertices $u$ and $v$ the colour $\phi(u)$ is different from the colour $\sigma(uv)\phi(v)$, where is $\sigma(uv)$ is the sign of the edge $uv$.
Edita Mácajová +2 more
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The b-Chromatic Number of Star Graph Families
Le Matematiche, 2010 In this paper, we investigate the b-chromatic number of central graph, middle graph and total graph of star graph, denoted by C(K1,n), M(K1,n) and T(K1,n) respectively.
Vivin J. Vernold, M. Venkatachalam
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T-Colorings, Divisibility and the Circular Chromatic Number
Discussiones Mathematicae Graph Theory, 2021 Let T be a T -set, i.e., a finite set of nonnegative integers satisfying 0 ∈ T, and G be a graph. In the paper we study relations between the T -edge spans espT (G) and espd⊙T(G), where d is a positive integer and d⊙T={0≤t≤d(maxT+1):d|t⇒t/d∈T}.d \odot T =
Janczewski Robert +2 more
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Advances in Mathematics, 1999 From the article: We consider graphs \({\mathcal G}=(X,R)\) where the vertex set \(X\) is a standard Borel space (i.e., a complete separable metrizable space equipped with its \(\sigma\)-algebra of Borel sets), and the edge relation \(R\subseteq X^2\) is ``definable,'' i.e., Borel, analytic, coanalytic, etc.
Kechris, A. S. +2 more
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Bounds on the Distinguishing Chromatic Number [PDF]
The Electronic Journal of Combinatorics, 2009 Collins and Trenk define the distinguishing chromatic number $\chi_D(G)$ of a graph $G$ to be the minimum number of colors needed to properly color the vertices of $G$ so that the only automorphism of $G$ that preserves colors is the identity. They prove results about $\chi_D(G)$ based on the underlying graph $G$.
Karen L. Collins +2 more
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On circulant chromatic number and circulant chromatic function
Discrete Mathematics, 2001 The circulant chromatic number (= star chromatic number, see \textit{A. Vince} [J. Graph Theory 12, No. 4, 551-559 (1988; Zbl 0658.05028)]) is accompanied with the new concept of a circulant chromatic function. Apart from basic facts and examples about this function the paper mainly investigates (in part with the help of this function) the relationship
Zhixiong Wang, Huishan Zhou
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Discrete Mathematics, 2002 A nice open problem is to find the minimum number of colors necessary to color the points of the Euclidean plane so that any two points of unit distance receive distinct colors. This number is known to be at least 4 (by finding a particular set of 6 points that require 4 colors) and 7 (by demonstrating a particular coloring of all the points).
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