#### İstanbul Center for Mathematical Sciences

3-Vertex Factors in Graphs
Saieed Akbari
Sharif University of Technology, Iran
Özet : Let $H$ be a graph. For a given graph $G$, an $H$-factor of $G$ is a spanning subgraph of $G$ whose components are isomorphic to $H$. In 1985, Akiyama and Kano conjectured that every 3-conneted cubic graph of order divisible by 3 has a $P_3$-factor. In this paper we conjecture that the aforementioned conjecture also holds for 3-connected 4-regular graphs. We show that the later conjecture implies the first one. In 2007 an infinite family of 2-connected cubic planar bipartite graphs of order divisible by 3 with no $P_3$-factor was constructed. In this paper, we present a simple construction for this result. Let $H = K_1\cup K_2$. We determine all graphs with maximum degree at most 3 admitting an $H$-factor. Also, we study those graphs which admit a $\overline{K_3}$-factor.
 Tarih : 18.08.2015 Saat : 10:30 Yer : IMBM Seminar Room, Bogazici University South Campus Dil : English