J. Korean Math. Soc. 2019; 56(1): 25-37
Online first article October 12, 2018 Printed January 1, 2019
https://doi.org/10.4134/JKMS.j180002
Copyright © The Korean Mathematical Society.
Hong Wang
The University of Idaho
Let $G$ be a bipartite graph with $(X,Y)$ as its bipartition. Let $B$ be a complete bipartite graph with a bipartition $(V_1,V_2)$ such that $X\subseteq V_1$ and $Y\subseteq V_2$. A {\em bi-packing} of $G$ in $B$ is an injection $\sigma$: $V(G) \rightarrow V(B)$ such that $\sigma (X)\subseteq V_1$, $\sigma (Y)\subseteq V_2$ and $E(G)\cap E(\sigma (G))=\emptyset$. In this paper, we show that if $G$ is a bipartite graph of order $n$ with girth at least 12, then there is a complete bipartite graph $B$ of order $n+1$ such that there is a bi-packing of $G$ in $B$. We conjecture that the same conclusion holds if the girth of $G$ is at least 8.
Keywords: packing, embedding, placement
MSC numbers: 05C70
2012; 49(6): 1259-1271
1998; 35(2): 449-463
2004; 41(4): 629-646
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd