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Journal of Combinatorial Optimization, ISSN 1382-6905, 4/2017, Volume 33, Issue 3, pp. 924 - 933
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 05/2018, Volume 88, Issue 1, pp. 146 - 153
For minimally k‐connected graphs on n vertices, Mader proved a tight lower bound for the number |Vk| of vertices of degree k in dependence on n and k. Oxley... 
minimally k‐connected graphs | tight | lower bounds | vertices of degree k | minimally k-connected graphs | MATHEMATICS
Journal Article
SIAM Journal on Computing, ISSN 0097-5397, 2012, Volume 41, Issue 5, pp. 1095 - 1109
  We present an $O(\log^2{k})$-approximation algorithm for the problem of finding a $k$-vertex connected spanning subgraph of minimum cost, where $n$ is the... 
Network design | Vertex-connectivity | Approximation algorithm | K-connected graph | Subroutines | Algorithms | Approximation | Mathematical analysis | Minimum cost | Graphs | Mathematical models | Optimization
Journal Article
Journal of the Korean Mathematical Society, ISSN 0304-9914, 2008, Volume 45, Issue 4, pp. 923 - 952
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 03/2014, Volume 166, pp. 263 - 268
A digraph is called rooted -edge-connected if it has a root node such that there exist arc-disjoint paths from to every other node and there is a path from... 
Highly [formula omitted]-tree-connected | Orientation | Rooted edge-connectivity | Highly k-tree-connected | MATHEMATICS, APPLIED | GRAPHS | Algorithms | Mathematical analysis | Roots | Rigid-body dynamics | Running | Graphs | Graph theory
Journal Article
Discrete Mathematics, ISSN 0012-365X, 12/2019, Volume 342, Issue 12, p. 111598
An edge of a -connected graph is said to be -contractible if the contraction of the edge results in a -connected graph. For a graph and a vertex of , let be... 
[formula omitted]-connected graph | Contraction-critically [formula omitted]-connected | Neighborhood | MATHEMATICS | k-connected graph | Contraction-critically k-connected
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 2/2016, Volume 31, Issue 2, pp. 669 - 685
In this paper we give improved approximation algorithms for some network design problems. In the bounded-diameter or shallow-light $$k$$ k -Steiner tree... 
k$$ k -edge connected | Network design | Steiner tree | Convex and Discrete Geometry | Approximation algorithms | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Operation Research/Decision Theory | Combinatorics | Combinatorial optimization | Optimization
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 05/2018, Volume 325, pp. 332 - 339
A connected graph is said to be -connected if it has more than vertices and remains connected whenever fewer than vertices are removed. Feng et al. (2017)... 
Signless Laplacian spectral radius | K-connected | Distance spectral radius | Distance signless Laplacian spectral radius | MATHEMATICS, APPLIED | TRACEABLE GRAPHS | TREES | HAMILTONIAN PROPERTIES | LAPLACIAN SPECTRAL-RADIUS | HARARY INDEX | WIENER POLARITY INDEX
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 10/2017, Volume 311, pp. 223 - 227
A total-colored graph is total rainbow connected if any two vertices are connected by a path whose edges and inner vertices have distinct colors. A graph is... 
Total rainbow coloring | Total rainbow connection number | Minimally total rainbow k-connected graph | MATHEMATICS, APPLIED | NUMBERS | COMPLEXITY
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 05/2016, Volume 205, pp. 101 - 108
A vertex subset of a connected graph is called a connected -path vertex cover ( ) if every path on vertices contains at least one vertex from , and the... 
Tree | Connected [formula omitted]-path vertex cover | Approximation algorithm | Girth | Weight | Connected k-path vertex cover | Algorithms
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 09/2014, Volume 174, pp. 92 - 101
Let be a positive integer and be a -connected graph. In 2009, Chartrand, Johns, McKeon, and Zhang introduced the of . An edge-coloured path is if its edges... 
Graph colouring | Rainbow (vertex) connection number | [formula omitted]-connected | k-connected | MATHEMATICS, APPLIED
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 08/2018, Volume 88, Issue 4, pp. 592 - 605
Let k and ℓ be positive integers. A cycle with two blocks c(k,ℓ) is a digraph obtained by an orientation of an undirected cycle, which consists of two... 
chromatic number | digraph coloring | strongly connected digraph | cycle with two blocks | MATHEMATICS | TREES | TOURNAMENTS | PATHS | CONJECTURE
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 01/2015, Volume 181, pp. 1 - 10
Given a simple undirected graph G and a positive integer k, the k-forcing number of G, denoted (G), is the minimum number of vertices that need to be initially... 
Nullity | Connected dominating sets | Connected domination number | k-forcing number | Zero forcing set | Zero forcing number | k-independence number | Rank | k-forcing | MATHEMATICS, APPLIED | INDEPENDENCE | SETS | DOMINATION
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 2009, Volume 410, Issue 19, pp. 1749 - 1764
We study clustering algorithms based on neighborhood graphs on a random sample of data points. The question we ask is how such a graph should be constructed in... 
Random geometric graph | Clustering | Connected component | Neighborhood graph | COMPUTER SCIENCE, THEORY & METHODS | CONNECTIVITY | Algorithms
Journal Article
ALGEBRAIC GEOMETRY, ISSN 2313-1691, 03/2019, Volume 6, Issue 2, pp. 196 - 233
A k-differential on a Riemann surface is a section of the kth power of the canonical line bundle. Loci of k-differentials with prescribed number and... 
CONNECTED COMPONENTS | MATHEMATICS | compactification | flat geometry | QUADRATIC-DIFFERENTIALS | k-differentials | strata | deformation | MODULI SPACES | SURFACES
Journal Article
Sensors (Switzerland), ISSN 1424-8220, 01/2016, Volume 16, Issue 1, p. 104
Coverage and connectivity are two important performance evaluation indices for wireless sensor networks (WSNs). In this paper, we focus on the connected target... 
Connected cover set | Connectivity | Heterogeneous wireless sensor networks (HWSNs) | K-coverage | CHEMISTRY, ANALYTICAL | INSTRUMENTS & INSTRUMENTATION | heterogeneous wireless sensor networks (HWSNs) | connectivity | connected cover set | k-coverage | LIFETIME | ENGINEERING, ELECTRICAL & ELECTRONIC
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 12/2014, Volume 173, Issue 1, pp. 65 - 82
In Pralle and Shpectorov (Adv Geom 7(1):1–17, 2007) the class of ovoidal hyperplanes in dual polar spaces of rank 4 is described. In this paper we observe that... 
Geometry | Simply connected | Affine | Biaffine | 51E24 | Mathematics | 20F05 | Flag-transitive | Hyperplane | Polar space
Journal Article
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