Mathematics

Running head: MATHEMATICS
MATHEMATICS

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MATHEMATICS
Table of Contents
Question no 6.............................................................................................................................2
Question no 7.............................................................................................................................3
Question no 11...........................................................................................................................4
Reference list..............................................................................................................................5

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MATHEMATICS
Question no 6.
In a graph to match perfectly, it is necessary to have all the vertices touched or used. Tutte"s
theorem always signifies towards matching with perfection. Tutte's theorem can perfectly
match the graph which contains edges not joined. A graph which is not directed can be
represented by G(V, E). Let M is a subset of E. Tutte"s theorem problem is based on:
Let us consider a set s arbitrarily. Let the unique element be C-S. In C to find a maximum
match, one vertex should not match. Let us consider that S subset of V.Let us match it with a
single vertex in S.So the necessary condition is
|s|>=q(G-S).where q represents no of odd components in G.(people.math.gatech.edu, 2019)
The sketch gives proof that it is a sufficient condition. Phi or null is not an even set in G.And
the odd set is |v(G)|. The maximal wrong edge can determine the bad in the complement
graph of G, a method of searching bad set and its formation. There are three claims to
commemorate the three points. The lousy set with the implementation of three claims is
shown below.