Results 11 to 20 of about 84,087 (307)
Physical Review Letters, 2002 We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high connectivity are uncolorable.
R. MULET +3 more
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Journal of Combinatorics, 2023 Given a graph G, the graph associahedron is a simple convex polytope whose face poset is based on the connected subgraphs of G. With the additional assignment of a color palette, we define the colorful graph associahedron, show it to be a collection of simple abstract polytopes, and explore its properties.
Devadoss, Satyan L., Smith, Mia
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Algorithmica, 2017 In this paper we study the number of vertex recolorings that an algorithm needs to perform in order to maintain a proper coloring of a graph under insertion and deletion of vertices and edges. We present two algorithms that achieve different trade-offs between the number of recolorings and the number of colors used.
Barba, Luis +6 more
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Proceedings of the ACM Multimedia 2017 Workshop on South African Academic Participation, 2017 We present a means of formulating and solving graph coloring problems with probabilistic graphical models. In contrast to the prevalent literature that uses factor graphs for this purpose, we instead approach it from a cluster graph perspective. Since there seems to be a lack of algorithms to automatically construct valid cluster graphs, we provide ...
Streicher, Simon, Preez, Johan du
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Journal of Knot Theory and Its Ramifications, 2001 Coloring invariants for spatial graphs are defined, inspired by Fox colorings of knots and links. A new proof of a the nontriviality of Suzuki's n-theta curves is given. Necessary and sufficient conditions for colorings of θn-curves are described in terms of an Alexander polynomial defined by Litherland.
McAtee, Jenelle +2 more
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Weighted Graph Colorings [PDF]
Journal of Statistical Physics, 2009 We study two weighted graph coloring problems, in which one assigns $q$ colors to the vertices of a graph such that adjacent vertices have different colors, with a vertex weighting $w$ that either disfavors or favors a given color. We exhibit a weighted chromatic polynomial $Ph(G,q,w)$ associated with this problem that generalizes the chromatic ...
Chang, Shu-Chiuan, Shrock, Robert
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Embedding Graphs into Colored Graphs [PDF]
Transactions of the American Mathematical Society, 1988 If X X is a graph, κ \kappa a cardinal, then there is a graph Y Y such that if the vertex set of Y Y is κ \kappa -colored, then there exists a monocolored induced copy of X X ; moreover, if X X does not contain a complete graph on
Hajnal, András, Komjáth, P.
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Multi-colored spanning graphs [PDF]
Theoretical Computer Science, 2016 We study a problem proposed by Hurtado et al. (2016) motivated by sparse set visualization. Given $n$ points in the plane, each labeled with one or more primary colors, a \emph{colored spanning graph} (CSG) is a graph such that for each primary color, the vertices of that color induce a connected subgraph.
Akatya, Hugo +2 more
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On irreducible no-hole L(2, 1)-coloring of Cartesian product of trees with paths
AKCE International Journal of Graphs and Combinatorics, 2020 An L(2, 1)-coloring of a graph G is a mapping such that for all edges uv of G, and if u and v are at distance two in G. The span of an L(2, 1)-coloring f of G, denoted by span(f), is max The span of G, denoted by is the minimum span of all possible L(2 ...
Nibedita Mandal, Pratima Panigrahi
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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
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