Chord theorems on graphs

Details Chord theorems on graphs Chord theorems on graphs

2007-02-27

arxiv.org/abs/math/0702805v2

Mathematics

Group Theory

10 pages

Scientific paper

The Horizontal Chord Theorem states that if a continuous curve connects points $A$ and $B$ in the plane, then for any integer $k$ there are points $C$ and $D$ on the curve such that $\overrightarrow{AB}=k \overrightarrow{CD}$. In this note, we discuss a few combinatorial-analysis problems related to this theorem and introduce a different formulation that gives way to generalizations on graphs.

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