The ally-reconstruction number of a tree with five or more vertices is
that the ally-reconstruction number is defined for all trees on three or more ver- ... and Plantholt made in [6] is that all trees with five or more vertices have ally-.
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On the edge-reconstruction number of a tree
Dec 5, 2013 ... and more recent ones which we carried out, we show that, apart from three known ... equal to 3 even though their class (vertex) reconstruction number was equal to 2. In [13], Molina started ..... Figure 5: The graph G as H − b + e3 ≃ H − c + e3. 8 ...... The ally-reconstruction number of a tree with five or more ...
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A survey of some open questions in reconstruction numbers
graphs with at least three vertices are reconstructible from their decks. A graph G has ... Some of the results obtained also seemed to give more evidence in favour of the truth of the ... that almost every graph has ally reconstruction number equal to 3. (It is clear that ..... The ally reconstruction number of a tree with five or more ...
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Reconstruction Numbers of Small Graphs - RIT computer science
Mar 6, 2008 ... Any graph on 3 or more vertices can be reconstructed its ..... The ally- reconstruction number of a tree with five or more vertices is three. J. Graph ...
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Edge Reconstruction Number of Disconnected Graph - CiteSeerX
and Plantholt in [2], and is referred to as the ally reconstruction number by Myrvold in [4]. ... the vertex reconstruction number of a graph is always three or more. .... not, and thus the replacing edge e1 joins an isolate and a tree with e(C1 )−1 .... e1 must join C1 − e1 to form a component isomorphic to C1, and thus G ≈ H. 5 ...
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Graph Reconstruction - Some New Developments - AKCE
Jun 7, 2004 ... RC: Any graph G with at least 3 vertices is uniquely determined up to ..... The ally reconstruction number of a tree with five or more vertices is.
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Degree-associated reconstruction number of graphs - Mathematics
Mar 10, 2010 ... a star or the 6-vertex tree with four leaves and maximum degree 3. ... the family T of trees, Harary and Lauri [5] proved that the class reconstruction number of .... Hence the parameters differ by more than 1 when drn(G) = 1.
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Families of pairs of graphs with a large number of common cards
Apr 27, 2009 ... the path on n vertices (when n=0, then both of these graphs are the null graph). ... number of cards given must then be the ally reconstruction number. ... has proved that rn(G)=3 for any tree of order five or more [26] and also ...
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Complexity Results in Graph Reconstruction - Computer Science
Oct 10, 2004 ... 5. For all k ≥ 2, GI ≡p iso k-LEDc. For many of these results, even ... Similar to the definition of reconstruction numbers vrn∃(G) [HP85] and ern∃(G) ... undirected graph on at least three vertices is determined uniquely (up to isomorphism ... of graphs—including graphs of bounded degree, partial k-trees for ...
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Graph Theory Notes - University of Warwick
V = {1,2,3,4,5} and E = {{1,2},{2,3},{3,4},{4,5}} define a graph with 5 vertices and 4 ... The degree of v ∈ V (G), denoted deg(v), is the number of edges incident to v. ..... proposed a more compact way of describing a labelled tree. .... ally hard. For cographs, it allows an efficient implementation which is based on the following.
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Global, Dense Multiscale Reconstruction for a Billion Points
minimum number of variables with respect to the the tree structure. Together with the ... ally optimize a surface representation. However, they do .... 0 else. (5). With R and W as above wi(c) ≈. 4. 3 πσ3 i Rh(pi − c) , and. (6) fi(c) ≈. 1 wi. 4. 3 πσ3 ..... compute vertex positions leads to a more faithful reconstruction of edges and ...
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Full Text (PDF format) - International Press
particular we review and extend results on the reconstruction of the ... 3. 2.2. Spanning trees. 4. 2.3. Characteristic polynomials. 5. 3. Networks. 6 .... For networks on more general surfaces we are beginning ... Many of the results discussed below are .... Suppose B is a nonempty set boundary vertices and u is a function on.
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Recovering the tree-like trend of evolution despite - arXiv.org
Jun 18, 2012 ... evolution where genetic material is transferred between two more or less ... ear number of) LGT events per gene tree. ... ally efficient reconstruction method and provides insight into the .... such that 1) the degree of all internal vertices Vs − Ls is exactly 3 ... The branch lengths will play a role in Section 5.
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Reconstructing Loopy Curvilinear Structures Using - Bjoern Andres
ally assume a tree topology for the networks. At the heart of our .... radius—as described in [5]. Figure 3. A loopy graph with a single root vertex v (in red). Al-.
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Degree Associated Edge Reconstruction Number of Graphs with
subgraph without end vertices of a graph G which is not a tree is the pruned ... Harary and Plantholt [3] defined the reconstruction number, rn(G), to be the ..... degree sum of the two vertices to be joined will be 1, 2, 3, 4, 5, 6(if | ˜G| > 3 and r > 6), ..... [7] W.J. Myrvold, The Ally and Adversary Reconstruction Problems, Ph.D.
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Trace Complexity of Network Inference - Department of Computer
much smaller (and more realistic) number of traces, making them potentially solvable in .... perfect reconstruction of the topology of trees and of bounded de-.
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The Cophylogeny Reconstruction Problem is NP-Complete∗
Sep 7, 2009 ... vertex or edge of the host tree and can be constructed using the four types of events. The objective of the cophylogeny reconstruction problem is to find one or more ... associated with each solution where the entries indicate the number of .... Figure 3: The assignment gadget is set to true if α1 occurs prior to ...
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cs.princeton.edu - Satyen Kale
Noise Tolerance of Expanders and Sublinear Expander Reconstruction. Satyen Kale ... of numbers is sorted, or that a large graph is a tree. These properties are ...
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ExactMP: An Efficient Parallel Exact Solver for Phylogenetic Tree
... of phylogenetic tree reconstruction using maximum parsimony, (2) a new up- ... phylogenetic tree is selected in three steps: (a) all possible tree topologies are ...
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Maximum likelihood of evolutionary trees: hardness and
Two frequently used reconstruction criteria are maximum parsimony ... In this paper we explore three extensions of the intractability result. First .... of the ML tree, nis the number of vertices in the original graph, ..... While the root has subtrees with more thanf 5. 2 ..... ally long sample size suffices to guarantee that the ML tree.
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