Results 11 to 20 of about 2,969,729 (299)
On the Independent Set Sequence of a Tree [PDF]
The Electronic Journal of Combinatorics, 2021 Alavi, Malde, Schwenk and Erdős asked whether the independent set sequence of every tree is unimodal. Here we make some observations about this question. We show that for the uniformly random (labelled) tree, asymptotically almost surely (a.a.s.) the initial approximately 49.5% of the sequence is increasing while the terminal approximately 38.8% is ...
Abdul Basit 0001, David J. Galvin
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On the status sequences of trees
Theoretical Computer Science, 2021 The status of a vertex $v$ in a connected graph is the sum of the distances from $v$ to all other vertices. The status sequence of a connected graph is the list of the statuses of all the vertices of the graph. In this paper we investigate the status sequences of trees.
Aida Abiad +2 more
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Extremal Trees with Fixed Degree Sequence [PDF]
The Electronic Journal of Combinatorics, 2021 The greedy tree $\mathcal{G}(D)$ and the $\mathcal{M}$-tree $\mathcal{M}(D)$ are known to be extremal among trees with degree sequence $D$ with respect to various graph invariants. This paper provides a general theorem that covers a large family of invariants for which $\mathcal{G}(D)$ or $\mathcal{M}(D)$ is extremal. Many known results, for example on
Eric Ould Dadah Andriantiana +2 more
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Packing Tree Degree Sequences [PDF]
Graphs and Combinatorics, 2019 AbstractA degree sequence is a list of non-negative integers, $${D = d_1, d_2, \ldots , d_n}$$D=d1,d2,…,dn. It is called graphical if there exists a simple graph G such that the degree of the ith vertex is $$d_i$$di; G is then said to be a realization of D. A tree degree sequence is one that is realized by a tree.
Kristóf Bérczi +3 more
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Sequencing the fungal tree of life [PDF]
New Phytologist, 2011 Sequencing the Fungal Tree of Life F. Martin 1 , D. Cullen 2 , D. Hibbett 3 , A. Pisabarro 4 , J. W. Spatafora 5 , S. E. Baker 6,7, I. V. Grigoriev 7 UMR INRA/UHP 1136, Interactions Arbres/Micro-Organismes, INRA-Nancy, 54280 Champenoux, France University of Wisconsin-Madison, Madison, WI, USA Clark University, Worcester, MA, USA Department of Agrarian ...
Martin, Francis +6 more
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Trees and Meta-Fibonacci Sequences [PDF]
The Electronic Journal of Combinatorics, 2009 For $k>1$ and nonnegative integer parameters $a_p, b_p$, $p = 1..k$, we analyze the solutions to the meta-Fibonacci recursion $C(n)=\sum_{p=1}^k C(n-a_p-C(n-b_p))$, where the parameters $a_p, b_p$, $p = 1..k$ satisfy a specific constraint. For $k=2$ we present compelling empirical evidence that solutions exist only for two particular families of ...
Abraham Isgur +2 more
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Bisection of trees and sequences
Discrete Mathematics, 1993 A bisectable graph \(G\) is the edge-disjoint union of two isomorphic subgraphs. The authors show a quantified version of the fact that any tree with \(e\) edges contains a bisectable subgraph with (asymptotically) almost all edges.
Noga Alon, Yair Caro, Ilia Krasikov
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AllSome Sequence Bloom Trees [PDF]
Journal of Computational Biology, 2016 Abstract The ubiquity of next generation sequencing has transformed the size and nature of many databases, pushing the boundaries of current indexing and searching methods. One particular example is a database of 2,652 human RNA-seq experiments uploaded to the Sequence Read Archive.
Sun, Chen +3 more
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Visualization of Barrier Tree Sequences
IEEE Transactions on Visualization and Computer Graphics, 2006 Dynamical models that explain the formation of spatial structures of RNA molecules have reached a complexity that requires novel visualization methods that help to analyze the validity of these models. Here, we focus on the visualization of so-called folding landscapes of a growing RNA molecule. Folding landscapes describe the energy of a molecule as a
Christian Heine 0002 +4 more
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Assembly Sequence Planning by Probabilistic Tree Transformation
Emitter: International Journal of Engineering Technology, 2018 Various types of computer systems including CAD/CAM systems have been introduced in machine industry. Some of the systems can handle assembly sequence planning, however it requires long time for planning.
Takeshi Murayama +3 more
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