%0 Journal Article
%T $(r)$-Pancyclic, $(r)$-Bipancyclic and Oddly $(r)$-Bipancyclic Graphs
%A Abdollah Khodkar
%A Oliver Sawin
%A Lisa Mueller
%A WonHyuk Choi
%J Mathematics
%D 2015
%I arXiv
%X A graph with $v$ vertices is $(r)$-pancyclic if it contains precisely $r$ cycles of every length from 3 to $v$. A bipartite graph with even number of vertices $v$ is said to be $(r)$-bipancyclic if it contains precisely $r$ cycles of each even length from 4 to $v$. A bipartite graph with odd number of vertices $v$ and minimum degree at least 2 is said to be oddly $(r)$-bipancyclic if it contains precisely $r$ cycles of each even length from 4 to $v-1$. In this paper, using computer search, we classify all $(r)$-pancyclic and $(r)$-bipancyclic graphs with $v$ vertices and at most $v+5$ edges. We also classify all oddly $(r)$-bipancyclic graphs with $v$ vertices and at most $v+4$ edges.
%U http://arxiv.org/abs/1510.03052v1