Results 11 to 20 of about 11,868 (264)
Circular Coloring and Fractional Coloring in Planar Graphs [PDF]
Journal of Graph Theory, 2020 AbstractWe study the following Steinberg‐type problem on circular coloring: for an odd integer , what is the smallest number such that every planar graph of girth without cycles of length from to admits a homomorphism to the odd cycle (or equivalently, is circular ‐colorable).
Xiaolan Hu, Jiaao Li
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Fractional Zero Forcing via Three-color Forcing Games [PDF]
Discrete Applied Mathematics, 2015 An $r$-fold analogue of the positive semidefinite zero forcing process that is carried out on the $r$-blowup of a graph is introduced and used to define the fractional positive semidefinite forcing number. Properties of the graph blowup when colored with
Hogben, Leslie +4 more
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Improved Distributed Fractional Coloring Algorithms [PDF]
, 2021 We prove new bounds on the distributed fractional coloring problem in the LOCAL model. Fractional $c$-colorings can be understood as multicolorings as follows. For some natural numbers $p$ and $q$ such that $p/q\leq c$, each node $v$ is assigned a set of at least $q$ colors from $\{1,\dots,p\}$ such that adjacent nodes are assigned disjoint sets of ...
Magnús M. Halldórsson +2 more
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Fractional hypergraph coloring [PDF]
We investigate proper $(a:b)$-fractional colorings of $n$-uniform hypergraphs, which generalize traditional integer colorings of graphs. Each vertex is assigned $b$ distinct colors from a set of $a$ colors, and an edge is properly colored if no single color is shared by all vertices of the edge.
Margarita Akhmejanova, Sean Longbrake
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On Coloring of graph fractional powers [PDF]
Discrete Mathematics, 2008 \noindent Let $G$ be a simple graph. For any $k\in N$, the $k-$power of $G$ is a simple graph $G^k$ with vertex set $V(G)$ and edge set $\{xy:d_G(x,y)\leq k\}$ and the $k-$subdivision of $G$ is a simple graph $G^{\frac{1}{k}}$, which is constructed by replacing each edge of $G$ with a path of length $k$.
Moharram N. Iradmusa
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Coloring, list coloring, and fractional coloring in intersections of matroids [PDF]
CombinatoricaAbstract It is known that in matroids the difference between the chromatic number and the fractional chromatic number is smaller than 1, and that the list chromatic number is equal to the chromatic number. We investigate the gap within these pairs of parameters for hypergraphs that are the intersection of a given ...
Ron Aharoni +3 more
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Distributed Algorithms for Fractional Coloring [PDF]
, 2021 In this paper we study fractional coloring from the angle of distributed computing. Fractional coloring is the linear relaxation of the classical notion of coloring, and has many applications, in particular in scheduling. It was proved by Hasemann, Hirvonen, Rybicki and Suomela (2016) that for every real $ >1$ and integer $ $, a fractional ...
Nicolás Bousquet +2 more
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Borel fractional colorings of Schreier graphs [PDF]
Annales Henri Lebesgue, 2022 Let Γ be a countable group and let G be the Schreier graph of the free part of the Bernoulli shift Γ↷2 Γ (with respect to some finite subset F⊆Γ). We show that the Borel fractional chromatic number of G is equal to 1 over the measurable independence number of G.
Anton Bernshteyn
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Fractional DP-Colorings of Sparse Graphs [PDF]
Journal of Graph Theory, 2018 AbstractDP‐coloring (also known as correspondence coloring) is a generalization of list coloring developed recently by Dvořák and Postle [J. Combin. Theory Ser. B 129 (2018), pp. 38–54]. In this paper we introduce and study the fractional DP‐chromatic number .
Anton Bernshteyn +2 more
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Colorings with Fractional Defect [PDF]
, 2017 Consider a coloring of a graph such that each vertex is assigned a fraction of each color, with the total amount of colors at each vertex summing to $1$. We define the fractional defect of a vertex $v$ to be the sum of the overlaps with each neighbor of $v$, and the fractional defect of the graph to be the maximum of the defects over all vertices. Note
Wayne Goddard, Honghai Xu
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