Graph designs for all graphs with six vertices and eight edges are discussed. The existence of these graph designs are completely solved except in two possible cases of order 32.
In this paper, we discuss the G-decomposition of λKv （G-GD）, （v）） into five graphs with six vertices and eight edges. We present some recursive structures and a number of G-designs of small orders, holey G- desi...In this paper, we discuss the G-decomposition of λKv （G-GD）, （v）） into five graphs with six vertices and eight edges. We present some recursive structures and a number of G-designs of small orders, holey G- designs, and incomplete G-designs are constructed. Finally, the spectrum of the existence of G-GD）λ（v） is determined.展开更多
In this paper, we first introduce a special structure that allows us to construct a large set of resolvable Mendelsohn triple systems of orders 2q ＋ 2, or LRMTS（2q ＋ 2）, where q = 6t ＋ 5 is a prime power. Using a...In this paper, we first introduce a special structure that allows us to construct a large set of resolvable Mendelsohn triple systems of orders 2q ＋ 2, or LRMTS（2q ＋ 2）, where q = 6t ＋ 5 is a prime power. Using a computer, we find examples of such structure for t C T = {0, 1, 2, 3, 4, 6, 7, 8, 9, 14, 16, 18, 20, 22, 24}. Furthermore, by a method we introduced in [13], large set of resolvable directed triple systems with the same orders are obtained too. Finally, by the tripling construction and product construction for LRMTS and LRDTS introduced in [2, 20, 21], and by the new results for LR-design in [8], we obtain the existence for LRMTS（v）and LRDTS（v）, where v = 12（t ＋ 1） mi≥0（2.7mi＋1）mi≥0（2.13ni＋1）and t∈T,which provides more infinite family for LRMTS and LRDTS of even orders.展开更多
基金Supported by the Natural Science Foundation of China （No.10371031） and Natural Science Foundation of Hebei （No.103146）.
文摘Graph designs for all graphs with six vertices and eight edges are discussed. The existence of these graph designs are completely solved except in two possible cases of order 32.
基金Supported by National Natural Science Foundation of China Grant 10971051,11171089Natural Science Foundation of Hebei Province Grant A2010000353
文摘In this paper, we discuss the G-decomposition of λKv （G-GD）, （v）） into five graphs with six vertices and eight edges. We present some recursive structures and a number of G-designs of small orders, holey G- designs, and incomplete G-designs are constructed. Finally, the spectrum of the existence of G-GD）λ（v） is determined.
基金the National Natural Science Foundation of China(No.10671055)Natural Science Foundation of Hebei(No.A2007000230)
文摘In this paper, we first introduce a special structure that allows us to construct a large set of resolvable Mendelsohn triple systems of orders 2q ＋ 2, or LRMTS（2q ＋ 2）, where q = 6t ＋ 5 is a prime power. Using a computer, we find examples of such structure for t C T = {0, 1, 2, 3, 4, 6, 7, 8, 9, 14, 16, 18, 20, 22, 24}. Furthermore, by a method we introduced in [13], large set of resolvable directed triple systems with the same orders are obtained too. Finally, by the tripling construction and product construction for LRMTS and LRDTS introduced in [2, 20, 21], and by the new results for LR-design in [8], we obtain the existence for LRMTS（v）and LRDTS（v）, where v = 12（t ＋ 1） mi≥0（2.7mi＋1）mi≥0（2.13ni＋1）and t∈T,which provides more infinite family for LRMTS and LRDTS of even orders.
