… In this note, we enumerate all nonisomorphic 3-factorizations of K10. … In the sequel, we
focus only on 3-factorizations of K10. It is well known that there are twenty one 3-regular graphs …

… 10 do not decompose K 10 . A close study of the main reason for failure to decompose K
10 was that only three copies of G are needed, thus for instance, K 10 cannot be decomposed …

… K10 Let K10 be the complete graph on 10 vertices. Then P is formed by the (10)= 45 edges
of K10 … Expand the first one via a and the second via ẞ to obtain 7 and 3 factorizations of the …

… of the edges of K10, let R, G, B denote the resulting red, green and blue spanning subgraphs,
and let AR, AG, AB denote their adjacency matrices. If u, v are vertices of K10, then v is …

It is shown that if F 1 , F 2 , …, F t are bipartite 2‐regular graphs of order n and α 1 , α 2 , …, α
t are positive integers such that α 1 + α 2 + ⋅ + α t = (n − 2)/2, α 1 ≥3 is odd, and α i is even …

… Several authors investigated 3-factorizations of λKv with a certain automorphism group, see
eg [1, 24]. In general, decompositions of λKv is also a widely studied problem, see eg [12, 13…

… of 3-factorizations of Kn is given in [10]. Resolvable block designs of order v with block size
k º 4 and index º 1 are equivalent to 3-factorizations of … family of uniform 3factorizations of Kn, …

… For t = 3, most such decompositions correspond to 3-factorizations of K(3) v . There are
also … We note however that the Berge cycles in these decompositions are not required to be …

… K 10 for many reasons. The graph G 6 contains K 4 but its independence number is 3. The
argument that the remaining two graphs fail to decompose K 10 … to decompose K 10 to cubic …

… In this letter we have studied a universal splitting of string and particle amplitudes into product
of … current, we can arrive at different 3-factorizations. For the former case, we choose m = 2 …