TEERADEJ KITTIPASSORN, Frustrated Triangles.
Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok, Thailand
Email:[email protected]
A graph is a collection of vertices and edges connecting some pairs of the vertices. We say that a triple of vertices in a graph is a frustrated triangle if it induces an odd number of edges, i.e. if it contains either one or three edges. We study the set Fn ⊂ [0,(n
3
)] of
possible number of frustrated triangles in a graph onn vertices. Observe that 0∈Fn since the empty graph (the graph with no edges) has no frustrated triangles. A natural question arises: what’s the next number in the set? In particular, does Fn always contain 1? We will answer this question and investigate the structure ofFn. This is based on a joint work with Gábor Mészáros.
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