Given a simple graph G (V, E) and a positive number d, an Ld(2, 1)-labelling of G is a function f V(G) [0, oc) such that whenever x, y E V are adjacent, If(x)f(Y)l >2d, and whenever the distanceâ€¦ (More)

We show that symmetric Venn diagrams for n sets exist for every prime n, settling an open question. Until this time, n = 11 was the largest prime for which the existence of such diagrams had beenâ€¦ (More)

Let F âŠ‚ 2[n] be a family of subsets of {1, 2, . . . , n}. For any poset H , we say F is H-free if F does not contain any subposet isomorphic to H . Katona and others have investigated the behaviourâ€¦ (More)

Let m(n) be the largest number of (maximalj cliques in any graph on yt vertices. Some twenty years ago Erdiis and m(n)? Which graphs have m(n) cliques? In both questions. It is natural to ask similarâ€¦ (More)

The theory of integer Î»-labelings of a graph, introduced by Griggs and Yeh, seeks to model efficient channel assignments for a network of transmitters. To prevent interference, labels for nearbyâ€¦ (More)

Wei discovered that the independence number of a graph G is at least x,.(1 + d(v))-â€˜. It is proved here that if G is a connected triangle-free graph on n > 3 vertices and if G is neither an odd cycleâ€¦ (More)