[PDF] k-Connectivity Definition: G is k-connected

Chapter 5 Connectivity

Similarly a graph is k-edge connected if it has at least two vertices and no set For 2-edge-connected graphs

Section 4.1 Connectivity: Properties and Structure

Turáns Theorem and k-Connected Graphs

Indeed let G be such a graph and v ? V (G) one of its vertices. If w is any neighbor of v

Note On the k-diameter of k-regular k-connected graphs

Since for a cycle of length n we have d2(Cn) = n - 1 the assertion holds for k = 2. Thus suppose that k - 2 > 1 and define graph G as Cn_k+Z. H

4.2 k-connected graphs

(Whitney [1932]) A graph G having at least 3 vertices is 2-connected iff for all uv ? V(G) there exist internally disjoint u

On Franks conjecture on k-connected orientations

Mar 7 2022 We are going to define a graph G = G(?) such that there exists a k-connected orientation of G if and only if there is an assignment of the ...

k-Connectivity

Definition: G is k-connected if •

Characterising k-connected sets in infinite graphs

Note that while the definition of l–KpkKq formally depends on the choice of a good ?-sequence

The contractible subgraph of k-connected graphs

Tutte's proved that every 3-connected graph on more than four vertices contains an edge whose contraction yields a new 3-connected graph [T1].

EPFL

Nov 14 2019 Let G be a k-connected graph. Show using the definitions that if G is obtained from G by adding a new vertex V adjacent to at least k vertices ...

[PDF] 42 k-connected graphs

4 2 13 Theorem (Robbins 1939) A graph has a strong orientation iff it is 2-edge-connected Plus supporting definitions and examples 

[PDF] k-Connectivity

Definition: A block of a graph G is a maximally connected subgraph of G with no cut vertex The following things are true about blocks 1 G itself may be a 

[PDF] NOTE ON MINIMALLY k-CONNECTED GRAPHS - arXiv

A k-tree is either a complete graph on (k+1) vertices or given a k-tree G' with n vertices a k-tree G with (n+1) vertices can be constructed by introducing 

(PDF) Note on minimally k-connected graphs - ResearchGate

PDF A k-tree is either a complete graph on (k+1) vertices or given a k-tree G' with n vertices a k-tree G with (n+1) vertices can be constructed by

[PDF] Distribution of Contractible Edges in k-Connected Graphs - CORE

An edge xy of a k-connected graph G is said to be k-contractible if the graph G xy obtained from G by contracting xy is k-connected We derive several new

[PDF] Minimally 3-Connected Graphs* - CORE

No such characterization has previously been available DEFINITION A k-connected graph G is minimally k-connected (mkc) if it has no 

[PDF] Chapter 5 Connectivity

Similarly a graph is k-edge connected if it has at least two vertices and no set of k ?1 edges is a separator The edge-connectivity of G denoted by K (G) 

[PDF] Turáns Theorem and k-Connected Graphs - Gwenaël Joret

Indeed let G be such a graph and v ? V (G) one of its vertices If w is any neighbor of v then by definition there is a stable set S of size ?(G)+1in G ? 

[PDF] Section 41 Connectivity: Properties and Structure - UPCommons

For results about infinite graphs and connectivity algorithms the reader [Th01] Every f(k)-connected graph (defined in Fact F41) with bipartite index

[PDF] The k-Connected subgraph Problem 21 Introduction

We survey approximation algorithms for the k-Connected Subgraph problem formally defined as follows k-Connected Subgraph Input: A directed/undirected graph