Balantidium coli (B. coli) is the only trophic ciliate of low virulence causing dysentery in human. However, may be due to their active motility and invasive nature, they have been rarely described to cause infection in extraintestinal sites also. We herein describe a case where trophozoites of B. coli were detected in urinary sediment examination of an elderly female presenting with mild fever, dysuria and hematuria for last 1 week. The parasites were identified by their characteristic morphology and rapid spiraling motility. This is only the third case described in literature to detect B. coli in urine sediment.

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Abstract. Paul Erdős and László Lovász proved in a landmark article that, for any positive integer k, up to isomorphism there are only finitely many maximal intersecting families of k−sets (maximal k−cliques). So they posed the problem of determining or estimating the largest number N (k) of the points in such a family. They also proved by means of an example that N (k) ≥ 2k − 2 + 1 2 2k−2 k−1 . Much later, Zsolt Tuza proved that the bound is best possible up to a multiplicative constant by showing that asymptotically N (k) is at most 4 times this lower bound. In this paper we reduce the gap between the lower and upper bound by showing that asymptotically N (k) is at most 3 times the Erdős-Lovász lower bound. Conjecturally, the explicit upper bound obtained in this paper is only double the lower bound.

A lambda colouring (or L(2, 1)−colouring) of a graph is an assignment of non-negative integers (with minimum assignment 0) to its vertices such that the adjacent vertices must receive integers at least two apart and vertices at distance two must receive distinct integers. The lambda chromatic number (or the λ number) of a graph G is the least positive integer among all the maximum assigned positive integer over all possible lambda colouring of the graph G. Here we have primarily shown that every graph with lambda chromatic number t can be embedded in a graph, with lambda chromatic number t, which admits a partition of the vertex set into colour classes of equal size. It is further proved that if an n−vertex graph with lambda chromatic number t ≥ 5, where n ≥ t + 1, contains maximum number of edges, then the vertex set of such graph admits an equitable partition. For such an admitted equitable partition there are either 0 or min{|A|, |B|} number of edges between each pair (A, B) of subsets (i.e. roughly, such partition is a "sparse like" equitable partition). Here we establish a classification result, identifying all possible n−vertex graphs with lambda chromatic number t ≥ 3, where n ≥ t + 1, which contain maximum number of edges. Such classification provides a solution of a problem posed more than two decades ago by John P. Georges and David W. Mauro.