EDGE-CUT CYCLES AND CUTTING NUMBERS OF CYCLES AND GRAPHS.

摘要

In this paper, we define the cutting number of a cycle, an edge-cut cycle and the cutting number of a simple connected graph. We determine several conditions that imply that a cycle is an edge-cut cycle. We determine the cutting numbers of bipartite graphs. We also examine lower and upper bounds for the sizes of edge sets in terms of the cutting number and the size of the vertex set.