Uniformly resolvable $(C_4, K_{1, 3})$-designs of order v and

In this paper we consider the uniformly resolvable decompositions of the complete graph $2K_v$ into subgraphs where each resolution class contains only blocks isomorphic to the same graph. We completely determine the spectrum for the cases in which all the resolution classes are either $C_4$ or $K_{1,3}$.

[1]  C. Colbourn,et al.  The CRC handbook of combinatorial designs , edited by Charles J. Colbourn and Jeffrey H. Dinitz. Pp. 784. $89.95. 1996. ISBN 0-8493-8948-8 (CRC). , 1997, The Mathematical Gazette.

[2]  Mario Gionfriddo,et al.  Uniformly resolvable H-designs with H = {P 3 ,P 4 } , 2014 .

[3]  Ernst Schuster,et al.  Small Uniformly Resolvable Designs for Block Sizes 3 and 4 , 2013 .

[4]  Ernst Schuster.  Uniformly resolvable designs with index one and block sizes three and four - with three or five parallel classes of block size four , 2009, Discret. Math..

[5]  Vitaly I. Voloshin,et al.  Hypergraphs and Designs , 2014 .

[6]  Alan C. H. Ling,et al.  Maximum uniformly resolvable designs with block sizes 2 and 4 , 2009, Discret. Math..

[7]  S. Vanstone,et al.  Class-uniformly resolvable pairwise balanced designs with block sizes two and three , 1991, Discrete Mathematics.

[8]  Mario Gionfriddo,et al.  On the existence of uniformly resolvable decompositions of Kv and Kv-I-I into paths and kites , 2013, Discret. Math..

[9]  Brett Stevens,et al.  The Hamilton–Waterloo problem for cycle sizes 3 and 4 , 2009 .

[10]  Rolf S. Rees,et al.  Uniformly resolvable pairwise balanced designs with blocksizes two and three , 1987, J. Comb. Theory, Ser. A.

[11]  Salvatore Milici,et al.  A note on uniformly resolvable decompositions of Kv and Kv-I into 2-stars and 4-cycles , 2013, Australas. J Comb..

[12]  Zsolt Tuza,et al.  Uniformly resolvable decompositions of Kv into P3 and K3 graphs , 2013, Discret. Math..

[13]  Gennian Ge,et al.  On uniformly resolvable designs with block sizes 3 and 4 , 2010, Des. Codes Cryptogr..

[14]  Giovanni Lo Faro,et al.  Resolvable 3-star designs , 2014, Discret. Math..