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The $r$-reduced Cutting Numbers of Cycles, Sequences of Cycles and Graphs Dr. Brad Bailey* and Dr. Dianna Spence, North Georgia College & State University Mathematics Department


Abstract

In this talk, we define the $r$-reduced cutting number of a cycle $C$ within graph $G$ to be the number of components in $G-E(C)$ with order at least $r$. Then the $r$-reduced cutting number of $G$ is the maximum of the $r$-reduced cutting number over all possible cycles in $G$. We determine the maximum and minimum number of edges in a graph with $n$ vertices and $r$-reduced cutting number $k$. We also define the $r$-reduced cutting number for an edge-wise disjoint sequence of cycles in a graph. Then the cutting power (at level $r$) of a graph is the shortest such sequence which has $r$-reduced cutting number at least 2.
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