Decomposable Twofold Triple Systems with Non-Hamiltonian 2-Block Intersection Graphs
نویسندگان
چکیده
منابع مشابه
Block-Intersection Graphs of Steiner Triple Systems
A Steiner triple system of order n is a collection of subsets of size three, taken from the n-element set {0, 1, ..., n−1}, such that every pair is contained in exactly one of the subsets. The subsets are called triples, and a block-intersection graph is constructed by having each triple correspond to a vertex. If two triples have a non-empty intersection, an edge is inserted between their vert...
متن کاملHamilton Decompositions of Block-Intersection Graphs of Steiner Triple Systems
Block-intersection graphs of Steiner triple systems are considered. We prove that the block-intersection graphs of non-isomorphic Steiner triple systems are themselves non-isomorphic. We also prove that each Steiner triple system of order at most 15 has a Hamilton decomposable block-intersection graph.
متن کاملDecomposing block-intersection graphs of Steiner triple systems into triangles
The problem of decomposing the block intersection graph of a Steiner triple system into triangles is considered. In the case when the block intersection graph has even degree, this is completely solved, while when the block intersection graph has odd degree, removal of some spanning subgraph of odd degree is necessary before the rest can be decomposed into triangles. In this case, some decompos...
متن کاملThe chromatic index of block intersection graphs of Kirkman triple systems and cyclic Steiner triple systems
The block intersection graph of a combinatorial design with block set B is the graph with B as its vertex set such that two vertices are adjacent if and only if their associated blocks are not disjoint. The chromatic index of a graph G is the least number of colours that enable each edge of G to be assigned a single colour such that adjacent edges never have the same colour. A graph G for which...
متن کاملThe watchman's walk of Steiner triple system block intersection graphs
A watchman’s walk in a graph G = (V,E) is a minimum closed dominating walk. In this paper, it is shown that the number of vertices in a watchman’s walk on the block intersection graph of a Steiner triple system is between v−3 4 and v−7 2 , for admissible v ≥ 15. Included are constructions to build a design that achieves the minimum bound for any admissible v.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2020
ISSN: 1077-8926
DOI: 10.37236/7969