Results 21 to 30 of about 2,185 (126)
Massively Parallel Algorithms for Distance Approximation and Spanners
, 2021 Over the past decade, there has been increasing interest in distributed/parallel algorithms for processing large-scale graphs. By now, we have quite fast algorithms -- usually sublogarithmic-time and often $poly(\log\log n)$-time, or even faster -- for a
Biswas, Amartya Shankha +4 more
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Progress on the adjacent vertex distinguishing edge colouring conjecture
, 2020 A proper edge colouring of a graph is adjacent vertex distinguishing if no two adjacent vertices see the same set of colours. Using a clever application of the Local Lemma, Hatami (2005) proved that every graph with maximum degree $\Delta$ and no ...
Joret, Gwenaël, Lochet, William
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Infinite motion and 2-distinguishability of graphs and groups [PDF]
, 2013 A group A acting faithfully on a set X is 2-distinguishable if there is a 2-coloring of X that is not preserved by any nonidentity element of A, equivalently, if there is a proper subset of X with trivial setwise stabilizer. The motion of an element a in
A Russell +25 more
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Distant sum distinguishing index of graphs
, 2017 Consider a positive integer $r$ and a graph $G=(V,E)$ with maximum degree $\Delta$ and without isolated edges. The least $k$ so that a proper edge colouring $c:E\to\{1,2,\ldots,k\}$ exists such that $\sum_{e\ni u}c(e)\neq \sum_{e\ni v}c(e)$ for every ...
Przybyło, Jakub
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Phase transition in the sample complexity of likelihood-based phylogeny inference [PDF]
, 2017 Reconstructing evolutionary trees from molecular sequence data is a fundamental problem in computational biology. Stochastic models of sequence evolution are closely related to spin systems that have been extensively studied in statistical physics and ...
Roch, Sebastien, Sly, Allan
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A proper total coloring distinguishing adjacent vertices by sums of some product graphs
, 2014 In this article, we consider a proper total coloring distinguishes adjacent vertices by sums, if every two adjacent vertices have different total sum of colors of the edges incident to the vertex and the color of the vertex. Pilsniak and Wozniak \cite{PW}
Choi, Hana +3 more
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On Computing Centroids According to the p-Norms of Hamming Distance Vectors [PDF]
, 2019 In this paper we consider the p-Norm Hamming Centroid problem which asks to determine whether some given strings have a centroid with a bound on the p-norm of its Hamming distances to the strings.
Chen, Jiehua +2 more
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Finding Cycles and Trees in Sublinear Time [PDF]
, 2011 We present sublinear-time (randomized) algorithms for finding simple cycles of length at least $k\geq 3$ and tree-minors in bounded-degree graphs. The complexity of these algorithms is related to the distance of the graph from being $C_k$-minor-free ...
Alon +20 more
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ADJACENT VERTEX DISTINGUISHING TOTAL COLORING OF GRAPHS WITH LOWER AVERAGE DEGREE
Taiwanese Journal of Mathematics, 2008 An adjacent vertex distinguishing total coloring of a graph $G$ is a proper total coloring of $G$ such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing total coloring of $G$ is denoted by $\chi''_{a}(G)$.
Wang, Weifan, Wang, Yiqiao
openaire +2 more sources
On the neighbour sum distinguishing index of planar graphs
, 2016 Let $c$ be a proper edge colouring of a graph $G=(V,E)$ with integers $1,2,\ldots,k$. Then $k\geq \Delta(G)$, while by Vizing's theorem, no more than $k=\Delta(G)+1$ is necessary for constructing such $c$. On the course of investigating irregularities in
Bonamy, Marthe, Przybyło, Jakub
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