2-Connected Graphs Definition 1 A graph is connected if for any two
The connectivity of G denoted ?(G) is the smallest size of a vertex set S such that G?S is disconnected or has only one vertex. Two paths connecting two
A Simple Test on 2-Vertex- and 2-Edge-Connectivity Arxiv Version
Theorem 1. Let C be a chain decomposition of a simple connected graph G. Then G is 2-edge-connected if and only if the chains in C partition E.
Chapter 5 Connectivity
A graph admits a strongly connected orientation if and only if it is 2-edge connected. Proof. Necessity: If a graph G is not connected then there is no
Circuit Covers of Cubic Signed Graphs
12 ?.?. 2559 circuit cover if and only if it is flow-admissible (i.e. has a nowhere-zero integer flow). ... A graph G is 2-edge-connected if G is.
On essentially 4-edge-connected cubic bricks
15 ?.?. 2563 a 2-edge-connected cubic graph each edge lies in a perfect matching. ... Theorem that the graph G - u - v is matchable if and only if no ...
On Franks conjecture on k-connected orientations
7 ??.?. 2565 Robbins [10] proved that a graph G admits a strongly connected orientation if and only if G is 2-edge-connected. The following extension to.
Twinless articulation points and some related problems
26 ?.?. 2562 strongly connected graph G is 2-edge-twinless-connected if
1.1. What is a graph? 1.1.2. Definition. A graph G is a triple (V(G) E
A graph is finite if its vertex set and edge set are finite. A graph G is connected if each pair of vertices in G belongs to a path;.
Coloring Drawings of Graphs
21 ?.?. 2563 for this property: we show that every 4-edge-connected graph and ... A drawing ? of a graph G has a face-2-coloring if and only if G is ...
Average connectivity of minimally 2-connected graphs and average
23 ?.?. 2561 for any minimally 2-edge-connected graph G. Once again the lower bound is readily seen to be attained if and only if G is a cycle.
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