Prove that every tree with two or more vertices is bichromatic?

Answer 1

Prove that the maximum vertex connectivity one can achieve with a graph G on n.

01.

Define a bipartite graph. Prove that a graph is bipartite if and only if it contains no

circuit of odd lengths.

Define a cut-vertex. Prove that every connected graph with three or more vertices

has at least two vertices that are not cut vertices.

Prove that a connected planar graph with n vertices and e edges has e - n + 2 regions.

02.

03.

04.

Define Euler graph. Prove that a connected graph G is an Euler graph if and only if

all vertices of G are of even degree.

Prove that every tree with two or more vertices is 2-chromatic.

05.

06.

07.

Draw the two Kuratowski's graphs and state the properties common to these graphs.

Define a Tree and prove that there is a unique path between every pair of vertices in a

tree.

If B is a circuit matrix of a connected graph G with e edge arid n vertices, prove

that rank of B=e-n+1.

08.

09.