REGULAR PARTITIONS OFGRAPHS bY School of Humanities and Sciences kSzemeridi, E
Previous researchers have demonstrated that striping heuristics produce very good (and, in some cases, asymptotically optimal) partitions for regular grid graphs. These earlier methods di#ered in the domains of application and the stripe-height selection process, and did not have polynomial run-time...
Partitions of sets of two-fold triple systems, and their relation to some strongly regular graphs LetX be a set ofv + 1 elements, wherev ( *20c v + 1 3)\\left( {\\begin{array}{*{20}c} {v + 1}\\\ 3\\\ \\end{array} } \\right)triples chosen fromX can be ... MAP ...
Derving Bipartite graphs from hypergraphs Proposition 1 Any regular uniform hypergraph HGk,d can be represented usefully by a bipartite graph BGn,m: the vertices V and the edges E of the hypergraph are the partitions of BG, and (v i , e j ) are connected with an edge if and only if ...
Clearly, all (exactly) balanced k-partitions of the n vertices are equally likely to be proper k-colorings. Therefore, E[X] is the number of balanced k-partitions, n!/(n/k)! k , times the probability that a random d-regular
Inequalities are obtained between the various parameters of a distance-regular graph. In particular, if k 1 is the valency and k 2 is the number of vertices at distance two from a given vertex, then in general k 1 k 2 . For distance-regular graphs of diameter at least four, k 1 =k...
A decomposition of a simple graph $G$ is a pair $(G,P)$ where $P$ is a set of subgraphs of $G$, which partitions the edges of $G$ in the sense that every edge of $G$ belongs to exactly one subgraph in $P$. If the elements of $P$ are indu... G Araujo-Pardo,C Rubio-...
Szemeredi's Regularity Lemma is a very useful tool of extremal combinatorics. Recently, several refinements of this seminal result were obtained for special, more structured classes of graphs. We survey these results in their rich combinatorial context. In particular, we stress the link to the ...
A natural generalization of a regular (or equitable) partition of a graph, which makes sense also for non-regular graphs, is the so-called weight-regular partition, which gives to each vertex u ∈ V a weight that equals the corresponding entry ν u of the Perron eigenvector ν . This ...
Strongly regular graphs with the same parameters as the symplectic graph We consider orbit partitions of groups of automorphisms for the symplectic graph and apply Godsil-McKay switching. As a result, we find four families of st... S Kubota - 《Graduate School of Information Sciences》 被引量:...