1
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
Which of the following statements is true for every planar graph on $$n$$ vertices?
A
The graph is connected
B
The graph is Eulerian
C
The graph has a vertex-cover of size at most $$3n/4$$
D
The graph has an independent set of size at least $$n/3$$
2
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
$$G$$ is a simple undirected graph. Some vertices of $$G$$ are of odd degree. Add a node $$v$$ to $$G$$ and make it adjacent to each odd degree vertex of $$G$$. The resultant graph is sure to be
A
Regular
B
Complete
C
Hamiltonian
D
Euler
3
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
$$G$$ is a graph on $$n$$ vertices and $$2n-2$$ edges. The edges of $$G$$ can be partitioned into two edge-disjoint spanning trees. Which of the following in NOT true for $$G$$?
A
For every subset of $$k$$ vertices, the induced subgraph has at most $$2k-2$$ edges
B
The minimum cut in $$G$$ has at least two edges
C
There are two edge-disjoint paths between every pair of vertices
D
There are two vertex-disjoint paths between every pair of vertices
4
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
A binary tree with $$n>1$$ nodes has $${n_1}$$, $${n_2}$$ and $${n_3}$$ nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbours.

$${n_3}$$ can be expressed as:

A
$${n_1}$$ $$+$$ $${n_1}$$ $$-$$ $$1$$
B
$${n_1}$$ $$-$$ $$2$$
C
$$\left[ {{{{n_1} + {n_2}} \over 2}} \right]$$
D
$${n_2}$$ $$-$$ $$1$$
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