Self-complementary graph decompositions
TL;DR: In this paper, the spectrum for the last self-complementary graph on at most 7 vertices has been found, and the spectrum of the first self-compensating graph is known.
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Abstract: A complementary decomposition of XKn into a graph G is an edge-disjoint decomposition of lKn into copies of G such that if each copy H of G is replaced by its complement in V(H) then the result is an edge-disjoint decomposition of XKn into copies of G° ; it is a selfcomplementary decomposition if G = Gf . The spectrum for the last self-complementary graph on at most 7 vertices is found.
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Citations
Large set of P3‐decompositions
Qingde Kang,Yanfang Zhang +1 more
TL;DR: This work obtains the existence spectrum of (n,P3,λ)‐LGD, which is a partition of the edges of λKn into subgraphs (G‐blocks), each of which is isomorphic to G.
3
Decomposition of lambda-fold complete graphs into a certain five-vertex graph.
Qiang Li,Yanxun Chang +1 more
- 01 Jan 2004
TL;DR: This paper completely solve the case when G = G18 and proves that the necessary condition λv(v− 1) ≡ 0 (mod 14) for the existence of a (λKv, G18)-design with any positive integer λ is also sufficient except for (v, λ) = (8, 1), (14, 1).
Edge-colored cube decompositions
TL;DR: In this paper, necessary and sufficient conditions on n, μ and G for the existence of a (K n,Q 3,G, μ) edge-colored graph decomposition were given.
2
On large sets of Pk-decompositions
TL;DR: In this paper, Combin et al. obtained a general result by using the finite fields, that is, if q,Pk, k −1)-LGD is an odd prime power, then there exists a
1
References
Balanced incomplete block designs and related designs
TL;DR: The read would be well advised to have knowledge of primWe roots and residua classes modultb primes, as well as of finite Gcllois ficlde5, necessary to understand the problems of inequality in this paper.
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Combinatorics of experimental design
Anne Penfold Street,Deborah J. Street +1 more
- 01 Jan 1987
TL;DR: In this paper, direct and recursive methods for the construction of combinatorial designs are described for the statistician through its discussion of how the designs currently used in experimental work have been obtained and through its coverage of other known and potentially useful designs.
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Decomposition of a complete multigraph into simple paths: Nonbalanced handcuffed designs
TL;DR: The condition λv(v − 1) ≡ 0 (mod 2m), v ⩾ m + 1 is obviously necessary for the existence of an edge disjoint decomposition of a complete multigraph λKv into isomorphic simple paths consisting of m edges each.
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