The inflation $G_{I}$ of a graph $G$ with $n(G)$ vertices and $m(G)$ edges is obtained from $G$ by replacing every vertex of degree $d$ of $G$ by a clique, which is isomorph to the complete graph $K_{d}$, and each edge $(x_{i},x_{j})$ of $G$ is replaced by an edge $(u,v)$ in such a way that $uin X_{i}$, $vin X_{j}$, and two different edges of $G$ are replaced by non-adjacent edges of $G_{I}$. T...

We study the orbit of R under the Bianchi group PSL2(OK), where K is an imaginary quadratic field. The orbit SK , called a Schmidt arrangement, is a geometric realisation, as an intricate circle packing, of the arithmetic of K. We define certain natural subgroups whose orbits generalise Apollonian circle packings, and show that SK , considered with orientations, is a disjoint union of all of th...

A famous conjecture (usually called Ryser’s conjecture), appeared in the Ph.D thesis of his student, J. R. Henderson [9], states that for an r-uniform r-partite hypergraph H, the inequality τ(H) ≤ (r − 1)·ν(H) always holds. This conjecture is widely open, except in the case of r = 2, when it is equivalent to Kőnig’s theorem [16], and in the case of r = 3, which was proved by Aharoni in 2001 [2]...

Prof. E. Arthurs Dr. M. Eden T. S. Huang Prof. P. Elias Dr. M. P. Schu'tzenberger F. Jelinek Prof. R. M. Fano S. Asano T. Kailath Prof. J. B. Dennis J. Borsuk D. H. Pratt Prof. S. W. Golomb D. C. Coll D. L. Reich Prof. E. M. Hofstetter H. S. Ekre B. Reiffen Prof. D. A. Huffman H. A. Ernst L. G. Roberts Prof. W. W. Peterson E. F. Ferretti J. L. Rosenfeld Prof. W. F. Schreiber R. G. Gallager I. G...

Given a group G and an automorphism ? of G, two elements x,y?G are said to be ?-conjugate if x=gy?(g)?1 for some g?G. The number equivalence classes is the Reidemeister R(?) ?, R(?)=? all automorphisms then have R?-property. A finite simple graph ? gives rise right-angled Artin A?, which has as generators vertices relations vw=wv only v w joined by edge in ?. We conjecture that non-abelian grou...