1 research outputs found
Even and Odd Cycles Passing a Given Edge or a Vertex
In this paper we provide some sufficient conditions for the existence of an
odd or even cycle that passing a given vertex or an edge in -connected or
-edge connected graphs. We provide some similar conditions for the existence
of an odd or even circuit that passing a given vertex or an edge in 2-edge
connected graphs. We show that if is a -connected -regular graph, , then every edge of is contained in an even cycle. We also prove
that in a -edge connected graph, if a vertex has odd degree, then there is
an even cycle containing this vertex