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Applied Mathematics and Computation, ISSN 0096-3003, 10/2017, Volume 311, pp. 223 - 227
A total-colored graph G is total rainbow connected if any two vertices are connected by a path whose edges and inner vertices have distinct colors. A graph G... 
Total rainbow coloring | Total rainbow connection number | Minimally total rainbow k-connected graph | MATHEMATICS, APPLIED | VERTEX-CONNECTION | NUMBERS | COMPLEXITY | ALGORITHMS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 03/2013, Volume 161, Issue 4-5, pp. 702 - 705
An edge-coloured graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colours. A graph G is called... 
Rainbow connection | Edge colouring | Minimally rainbow [formula omitted]-connected | Minimally rainbow k-connected | MATHEMATICS, APPLIED | MINIMUM DEGREE
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 11/2018, Volume 34, Issue 6, pp. 1589 - 1595
We show that, for every integer k >= 4, if M is a k-connected matroid and C is a circuit of M such that for every e is an element of C, M\e is not k-connected,... 
Minimally k-connected | Matroids | Cocircuits | MATHEMATICS
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
Czechoslovak Mathematical Journal, ISSN 0011-4642, 09/2012, Volume 62, Issue 3, pp. 637 - 644
An edge e of a k-connected graph G is said to be k-contractible (or simply contractible) if the graph obtained from G by contracting e (i.e., deleting e and... 
contractible edge | component | k-connected graph | minimally k-connected graph | MATHEMATICS
Journal Article
Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 2008, Volume 98, Issue 6, pp. 1311 - 1324
A matroid M is minimally k-connected if M is k-connected and, for every e ∈ E ( M ) , M \ e is not k-connected. It is conjectured that every minimally... 
Minimally k-connected | Matroids | Cocircuits | MATHEMATICS | GRAPHS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2008, Volume 308, Issue 4, pp. 597 - 602
An edge of a k -connected graph is said to be k -contractible if the contraction of the edge results in a k -connected graph. In this paper, we prove that a (... 
Minimally k-connected | Contractible edge | k-Connected graph | contractible edge | MATHEMATICS | k-connected graph | minimally k-connected
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 08/2017, Volume 85, Issue 4, pp. 814 - 838
A graph G has maximal local edge‐connectivity k if the maximum number of edge‐disjoint paths between every pair of distinct vertices x and y is at most k. We... 
local connectivity | coloring | vertex degree | minimally k‐connected | Brooks’ theorem | local edge‐connectivity | local edge-connectivity | minimally k-connected | MATHEMATICS | Brooks' theorem | Computer Science | Discrete Mathematics
Journal Article
Czechoslovak Mathematical Journal, ISSN 0011-4642, 9/2013, Volume 63, Issue 3, pp. 671 - 677
An edge e of a k-connected graph G is said to be k-removable if G — e is still k-connected. A subgraph H of a k-connected graph is said to be k-contractible if... 
Ordinary Differential Equations | 05C83 | 5-connected graph | Analysis | Convex and Discrete Geometry | 05C40 | Mathematics, general | Mathematics | minor minimally k -connected | Mathematical Modeling and Industrial Mathematics | contractible subgraph | minor minimally k-connected | MATHEMATICS
Journal Article
Electronic Notes in Discrete Mathematics, ISSN 1571-0653, 2002, Volume 11, pp. 20 - 29
An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. In this paper, we prove that a ( K 1... 
contractible edge | minimally k-connected | k-connected graph
Journal Article
Information Processing Letters, ISSN 0020-0190, 2011, Volume 111, Issue 23, pp. 1124 - 1129
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2008, Volume 308, Issue 12, pp. 2533 - 2543
Let G be a minimally k-connected graph with n nodes and m edges. Mader proved that if n ⩾ 3 k - 2 then m ⩽ k ( n - k ) , and for n ⩾ 3 k - 1 an equality is... 
Extremal graphs | Minimally k-outconnected graphs | MATHEMATICS | N-CONNECTED GRAPHS | minimally k-outconnected graphs | extremal graphs
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 03/2005, Volume 21, Issue 1, pp. 39 - 50
Let D=(V,E) be a minimally k-edge-connected simple directed graph. We prove that there is a function f(k) such that |V|≥f(k) implies |E|≤2k(|V|−k). We also... 
Edge-connectivity | Mathematics | Engineering Design | Combinatorics | Directed graphs | Minimally k -edge-connected | Minimally k-edge-connected | MATHEMATICS | minimally k-edge-connected | edge-connectivity | directed graphs | Graphs
Journal Article
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