Math Problem Statement
A Θgraph consists of three internally vertexdisjoint paths joining two vertices (because such a graph looks like Θ). To obtain the maximum size of a graph with order n and no Θsubgraphs, consider such a graph G such that it has a blocks which are isomorphic to K2 and b blocks which are cycles. Express n and the size m of G in terms of a, b and the lengths of such cycles. Derive an upper bound on m and show that this bound can be achieved. Answer. If n is odd, then the maximum number of edges in an nvertex graph with no Θsubgraphs is 23 (n − 1). What is the answer for even n?
Solution
Math Problem Analysis
Mathematical Concepts
Graph Theory
Cycle Graphs
Maximal Edge Graphs
Formulas
Maximum number of edges in a graph without Θsubgraphs
Theorems

Suitable Grade Level
Advanced Undergraduate
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