Results 51 to 60 of about 9,612,020 (345)
On the Chromatic Number of Disjointness Graphs of Curves [PDF]
International Symposium on Computational Geometry, 2018 Let $\omega(G)$ and $\chi(G)$ denote the clique number and chromatic number of a graph $G$, respectively. The {\em disjointness graph} of a family of curves (continuous arcs in the plane) is the graph whose vertices correspond to the curves and in which ...
J. Pach, István Tomon
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Weighted graphs: Eigenvalues and chromatic number
Electronic Journal of Graph Theory and Applications, 2016 We revisit Hoffman relation involving chromatic number $\chi$ and eigenvalues. We construct some graphs and weighted graphs such that the largest and smallest eigenvalues $\lambda$ dan $\mu$ satisfy $\lambda=(1-\chi)\mu.$ We study in particular the ...
Charles Delorme
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Induced subgraphs of graphs with large chromatic number. XII. Distant stars [PDF]
Journal of Graph Theory, 2017 The Gyárfás‐Sumner conjecture asserts that if H is a tree then every graph with bounded clique number and very large chromatic number contains H as an induced subgraph.
M. Chudnovsky, A. Scott, P. Seymour
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A Tight Bound on the Set Chromatic Number
Discussiones Mathematicae Graph Theory, 2013 We provide a tight bound on the set chromatic number of a graph in terms of its chromatic number. Namely, for all graphs G, we show that χs(G) > ⌈log2 χ(G)⌉ + 1, where χs(G) and χ(G) are the set chromatic number and the chromatic number of G ...
Sereni Jean-Sébastien +1 more
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List-Chromatic Number and Chromatically Unique of the Graph Kr2+Ok
Selecciones Matemáticas, 2019 In this paper, we determine list-chromatic number and characterize chromatically unique of the graph G = Kr2+k.
Le Xuan Hung
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Graceful Chromatic Number of Unicyclic Graphs
Journal of Physics: Conference Series, 2019 We consider that all graph in this paper are finite, simple and connected graph. A graceful k−coloring of a graph is a proper vertex coloring f : V(G) → {1, 2, …, k}, where k ≥ 2 which induces a proper edge coloring f’ : E(G) → {1, 2, …, k − 1} defined ...
R. Alfarisi +5 more
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Circular Chromatic Numbers and Fractional Chromatic Numbers of Distance Graphs
European Journal of Combinatorics, 1998 This paper studies the circular (or star) chromatic numbers and fractional chromatic numbers of distance graphs \(G(Z, D)\) for various sets \(D\) (being the graph with vertex set a subset of the integers, and two vertices \(x\), \(y\) being adjacent iff \(| x-y|\in D\)). Various specific cases are calculated, including all cases when \(| D|= 2\).
Chang, Gerard J. +2 more
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Trees with Certain Locating-chromatic Number
Journal of Mathematical and Fundamental Sciences, 2016 The locating-chromatic number of a graph G can be defined as the cardinality of a minimum resolving partition of the vertex set V(G) such that all vertices have distinct coordinates with respect to this partition and every two adjacent vertices in G are ...
Dian Kastika Syofyan +2 more
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On the chromatic number local irregularity of related wheel graph
Journal of Physics: Conference Series, 2019 A function f is called a local irregularity vertex coloring if (i) l:V(G)→{1,2,…,k} as vertex irregular k-labeling and w:V(G)→N , for every uv∈E(G),w(u)≠w(v) where w(u)=Συ∈N(u)l(υ) and (ii) max(l) = min{max{li}; livertex irregular labeling}.
Arika Indah Kristiana +5 more
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Monotone Chromatic Number of Graphs
International Journal of Analysis and Applications, 2020 For a graph G = (V, E), a vertex coloring (or, simply, a coloring) of G is a function C: V (G) → {1, 2, ..., k} (using the non-negative integers {1, 2, ..., k} as colors).
Anwar Saleh +3 more
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