Results 81 to 90 of about 8,657,296 (197)
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
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The chromatic number of heptagraphs
Journal of Graph TheoryAbstractA pentagraph is a graph without cycles of length 3 or 4 and without induced cycles of odd length at least 7, and a heptagraph is one without cycles of length less than 7 and without induced cycles of odd length at least 9. Chudnovsky and Seymour proved that every pentagraph is 3‐colorable.
Di Wu, Baogang Xu, Yian Xu
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Some Equal Degree Graph Edge Chromatic Number
MATEC Web of Conferences, 2016 Let G(V, E) be a simple graph and k is a positive integer, if it exists a mapping of f, and satisfied with f(e1)≠6 = f(e2) for two incident edges e1,e2∉E(G), f(e1)≠6=f(e2), then f is called the k-proper-edge coloring of G(k-PEC for short).
Liu Jun +4 more
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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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Coloring Some Finite Sets in ℝn
Discussiones Mathematicae Graph Theory, 2013 This note relates to bounds on the chromatic number χ(ℝn) of the Euclidean space, which is the minimum number of colors needed to color all the points in ℝn so that any two points at the distance 1 receive different colors. In [6] a sequence of graphs Gn
Balogh József +2 more
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The locating-chromatic number for Halin graphs
Communications in Combinatorics and Optimization, 2017 Let $G$ be a connected graph. Let $f$ be a proper $k$-coloring of $G$ and $\Pi=\{R_1,R_2,\ldots, R_k\}$ be an ordered partition of $V(G)$ into color classes. For any vertex $v$ of $G,$ define the {\em color code} $c_\Pi(v)$ of $v$ with respect to $\
I.A. Purwasih +4 more
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Discrete Mathematics, 1994 From the article: ``Taking the colors to be the positive integers, the greedy vertex-coloring algorithm can be described as follows. The vertices of a graph \(G\) are ordered and the algorithm assigns colors to the vertices in that order, giving each vertex the first ...
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Modular chromatic number of $C_m square P_n$ [PDF]
Transactions on Combinatorics, 2013 A modular $k$-coloring, $kge 2,$ of a graph $G$ without isolated vertices is a coloring of the vertices of $G$ with the elements in $mathbb{Z}_k$ having the property that for every two adjacent vertices of $G,$ the sums of the colors of the neighbors are
N. Paramaguru, R. Sampathkumar
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Oriented Incidence Colourings of Digraphs
Discussiones Mathematicae Graph Theory, 2019 Brualdi and Quinn Massey [6] defined incidence colouring while study- ing the strong edge chromatic index of bipartite graphs. Here we introduce a similar concept for digraphs and define the oriented incidence chromatic number.
Duffy Christopher +3 more
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Discrete Mathematics, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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