Every tree has a perfect matching.
False. Every tree does not necessarily have a perfect matching. In graph theory, a perfect matching is _________ ________ __________ ________ _______.
______ __________ ______ _____ ____ _____ __________ ____.
______ ___ _______ ________ __________ ______ ____ _________ ________ ___ __________ ____.
_________ _________ _______ _________ ________.
_________ ______ ____ ___ _________ ___ _______ _______ ____ ____.
________ ____ _____ __________ _____.
__________ _____ __________ ________ _____ _________ _______ _______.
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The vertex-covering number of an odd cycle is 1 more than its independence number.
If G is a k-connected graph having n vertices, what is the minimum size of G? Justify .
Every tree has a perfect matching.
For some nonnegative integers d1, d2, . . . , dn the sequence (max{d1, n}, d2, d3, . . . , dn) is graphic.
For the graph given in Q. 3(b), find the number of (v2, v5)-walks of length 3.
Draw a diagram, as nice as possible, of the line graph of the Petersen graph. Write the number of vertices, the number of edges, the minimum and maximum degrees of it.
Define a flow on the following network, having value at least 5.
