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Journal of the London Mathematical Society, ISSN 0024-6107, 06/2019, Volume 99, Issue 3, pp. 653 - 677
In this paper, we address the problem of packing large trees in Gn,p. In particular, we prove the following result. Suppose that T1,…,TN are n‐vertex trees,... 
05C05 (primary) | Mathematics - Combinatorics
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 07/2016, Volume 220, Issue 7, pp. 2590 - 2647
In this paper, we construct a family of algebraic cycles in Bloch's cycle complex over P1 minus three points, which are expected to correspond to multiple... 
14C25 | 33B30 | 05C05 | 11G55
Journal Article
Combinatorics Probability and Computing, ISSN 0963-5483, 2018, Volume 28, Issue 1, pp. 23 - 45
Consider a uniform random rooted labelled tree on n vertices. We imagine that each node of the tree has space for a single car to park. A number m <= n of cars... 
82B26 | Secondary 60J80 | 2010 Mathematics subject classification | Primary 60C05 | 05C05 | MATHEMATICS | STATISTICS & PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS | RANDOM-WALK | Automobiles | Family trees | Apexes | Phase transitions | Combinatorial analysis
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 01/2018, Volume 87, Issue 1, pp. 89 - 95
We show that a tree of order n has at most O(5n/4) nonisomorphic subtrees, and that this bound is best possible. We also prove an analogous result for the... 
extremal problem | trees | subtrees | nonisomorphic trees | 05C05 | MATHEMATICS
Journal Article
Combinatorica, ISSN 0209-9683, 2/2014, Volume 34, Issue 1, pp. 11 - 46
Considering systems of separations in a graph that separate every pair of a given set of vertex sets that are themselves not separated by these separations, we... 
Mathematics, general | Mathematics | 05C83 | Combinatorics | 05C05 | 05C40 | MATHEMATICS | SETS | Mathematics - Combinatorics
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 04/2019, Volume 99, Issue 2, pp. 428 - 446
Given an iterated function system (IFS) of contractive similitudes, the theory of Gromov hyperbolic graph on the IFS has been established recently. In the... 
20F65 (secondary) | 05C05 | 28A80 (primary) | MATHEMATICS | DIRICHLET FORMS | CANTOR SETS | RANDOM-WALKS | GRAPHS
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 05/2019, Volume 39, Issue 2, pp. 415 - 437
For a graph = ( ), a function : ( ) → {1, 2, . . ., } is a ranking for if ) = ) implies that every − path contains a vertex such that ) ). A minimal -ranking,... 
tree | coloring | minimal ranking | 05C05 | 05C15 | MATHEMATICS | RANKINGS
Journal Article
Journal of Discrete Mathematical Sciences and Cryptography, ISSN 0972-0529, 08/2019, Volume 22, Issue 6, pp. 1121 - 1127
Placing measurement units in the vertices of an electric power system is clearly associated to determining dominate set in a graph. "A set S ⊂ V is defined... 
Domination | Sunlet Graph | 05C69 | 05C05 | 05C40 | Power Domination number
Journal Article
Journal of Discrete Mathematical Sciences and Cryptography, ISSN 0972-0529, 08/2019, Volume 22, Issue 6, pp. 1101 - 1106
Halin graphs can be constructed from a tree non degree 2-vertices, embedded in the plane and pendant vertices are connected by outer cycle. This graph is 3-... 
Halin Graph | Independent Domination number | 05C69 | 05C05 | 05C40 | Domination number
Journal Article
Journal of Discrete Mathematical Sciences and Cryptography, ISSN 0972-0529, 08/2019, Volume 22, Issue 6, pp. 1113 - 1119
A Halin graph H is a planar and three connected graph. The Halin graph is constructed by joining all pendent vertices of tree into cycle. In this article we... 
Halin Graph | Independent Domination number | 05C69 | 05C05 | 05C40 | Domination number
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2019, Volume 39, Issue 1, pp. 157 - 170
A graph G is H-saturated if H is not a subgraph of G but the addition of any edge from the complement of G to G results in a copy of H. The minimum number of... 
tree | saturation number | 05C35 | 05C05 | saturation spectrum | Saturation number | Saturation spectrum | Tree | MATHEMATICS | SOS CONJECTURE
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 05/2017, Volume 107, Issue 5, pp. 887 - 899
We calculate the exact number of contours of size n containing a fixed vertex in d-ary trees and provide sharp estimates for this number for more general... 
Trees | Contours | PERCOLATION | SETS | ISING-MODEL | Cut Sets | Peierls | Catalan numbers | GRAPHS | 05Cxx | Theoretical, Mathematical and Computational Physics | Complex Systems | 05C30 | Physics | Geometry | 05-XX | Group Theory and Generalizations | 05C05 | 82-XX | PHYSICS, MATHEMATICAL | Computer science | Mathematics - Combinatorics
Journal Article
Selecta Mathematica, ISSN 1022-1824, 10/2019, Volume 25, Issue 4, pp. 1 - 28
We study the category whose objects are trees (with or without roots) and whose morphisms are contractions. We show that the corresponding contravariant module... 
16P70 | Mathematics, general | Mathematics | 55N33 | 05C05 | 55R80 | MATHEMATICS | CONFIGURATION-SPACES | MATHEMATICS, APPLIED | HOMOLOGY
Journal Article
Monatshefte für Mathematik, ISSN 0026-9255, 1/2017, Volume 182, Issue 1, pp. 51 - 63
The number of spanning trees in a class of directed circulant graphs with generators depending linearly on the number of vertices $$\beta n$$ β n , and in the... 
Spanning tree | 05C30 | Circulant graph | Mathematics, general | Mathematics | Cycle power graph | 05C05 | MATHEMATICS | NUMBER | LOOP NETWORKS | Mathematics - Combinatorics
Journal Article
Combinatorica, ISSN 0209-9683, 6/2016, Volume 36, Issue 3, pp. 313 - 332
We construct spanning trees in locally finite hyperbolic graphs that represent their hyperbolic compactification in a good way: so that the tree has at least... 
Mathematics, general | Mathematics | Combinatorics | 05C63 | 05C05 | 20F67 | MATHEMATICS | EMBEDDINGS | DIMENSION | SPACES
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 08/2018, Volume 38, Issue 3, pp. 811 - 828
A subtree of a tree is a central subtree of if has the minimum eccentricity in the join-semilattice of all subtrees of . Among all subtrees lying in the... 
tree | 05C22 | central subtree | least central subtree | 05C05 | Tree | Central subtree | Least central subtree | LOCATION | MATHEMATICS
Journal Article
Combinatorica, ISSN 0209-9683, 2/2014, Volume 34, Issue 1, pp. 47 - 60
Let G be a connected simple graph, let X⊆V (G) and let f be a mapping from X to the set of integers. When X is an independent set, Frank and Gyárfás, and... 
Mathematics, general | Mathematics | 05C70 | Combinatorics | 05C05 | MATHEMATICS
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 09/2019, Volume 67, Issue 9, pp. 1736 - 1749
Let G be a simple and undirected graph with Laplacian polynomial . In earlier works, some formulas for computing , and in terms of the number of vertices, the... 
Zagreb index | tree | 05C31 | Laplacian coefficient | 05C05 | MATHEMATICS | SMALLEST | GRAPHS | Polynomials | Computation | Apexes | Upper bounds
Journal Article
Combinatorica, ISSN 0209-9683, 4/2018, Volume 38, Issue 2, pp. 381 - 398
The connected tree-width of a graph is the minimum width of a tree-decomposition whose parts induce connected subgraphs. Long cycles are examples of graphs... 
05C12 | 05C83 | 05C40 | Mathematics, general | Mathematics | Combinatorics | 05C05 | 05C38 | MATHEMATICS
Journal Article
Combinatorica, ISSN 0209-9683, 2/2019, Volume 39, Issue 1, pp. 37 - 75
We show that all the tangles in a finite graph or matroid can be distinguished by a single tree-decomposition that is invariant under the automorphisms of the... 
05B35 | 05C83 | 05C40 | Mathematics, general | Mathematics | Combinatorics | 05C05 | 06A07 | MATHEMATICS | Image processing | Analysis
Journal Article
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