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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.
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참고문헌 (9)
참고문헌 신청
B. Bollobas / 1978 / Extremal Graph Theory / Academic Press, Inc
S. Brandt / 1995 / Graph theory, combinatorics, and algorithms, Vol. 1, 2 / Wiley-Intersci. Publ, Wiley :115~121
R. J. Faudree / 1981 / Embedding graphs in their complements, Czechoslovak Math / Czechoslovak Math. J 31(1):53~62
J.-L. Fouquet / 1993 / Mutual placement of bipartite graphs / Discrete Math 121:85~92
A. Gorlich / 2004 / A note on embedding graphs without short cycles / Discrete Math 286(1-2):75~77
S. Brandt / 1995 / Graph theory, combinatorics, and algorithms, Vol. 1, 2 / Wiley-Intersci. Publ, Wiley :115~121
R. J. Faudree / 1981 / Embedding graphs in their complements, Czechoslovak Math / Czechoslovak Math. J 31(1):53~62
J.-L. Fouquet / 1993 / Mutual placement of bipartite graphs / Discrete Math 121:85~92
A. Gorlich / 2004 / A note on embedding graphs without short cycles / Discrete Math 286(1-2):75~77
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