Mathematics

Professor Shailesh Tipnis
Illinois State University

For graphs $G$ and $H$, graph $G$ is said to admit an $H$-decomposition if the edges of $G$ can be partitioned into isomorphic copies of $H$.
Let $P_{4}$ denote the path on 4 vertices.We survey results that assert that certain graphs and multigraphs admit a $P_{4}$ decomposition. We also discuss related on-going work on decomposing even-regular graphs into regular spanning subgraphs each of which do not contain dense subgraphs.