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

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

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

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

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

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

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

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

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

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

contractible edge | minimally k-connected | k-connected graph

Journal Article

Information Processing Letters, ISSN 0020-0190, 2011, Volume 111, Issue 23, pp. 1124 - 1129

For an integer l ⩾ 2 , the l-connectivity κ l ( G ) of a graph G is defined to be the minimum number of vertices of G whose removal produces a disconnected...

Minimally [formula omitted]-connected graphs | Combinatorial problems | Connectivity | [formula omitted]-Connected graphs | Minimally k-connected graphs | l-Connectivity | Minimally (2, l) -connected graphs | (k, l) -Connected graphs | Minimally (2. l)-connected graphs | COMPUTER SCIENCE, INFORMATION SYSTEMS | (k.1)-Connected graphs

Minimally [formula omitted]-connected graphs | Combinatorial problems | Connectivity | [formula omitted]-Connected graphs | Minimally k-connected graphs | l-Connectivity | Minimally (2, l) -connected graphs | (k, l) -Connected graphs | Minimally (2. l)-connected graphs | COMPUTER SCIENCE, INFORMATION SYSTEMS | (k.1)-Connected graphs

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

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

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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