121671285
Enumeration of non-separable planar maps
124281571
On finite plane sets containing for every pair of points an equidistant point
Consider the set shown in Figure 1, consisting of the points 2 in E whose circular polar coordinates are ( 1 , T T / 3 ) , (1,0) , ( 1 , T T / 6 ) , ( 1 , T T / 3 ) , (1,TT/2) , ( \ T 2 , I T / 4 ) , and ( 0 , 0 ) . If this set lay on the union of two circles then at least three of the f i rs t five points listed above would lie together on one of these c i rc les , which must therefore be the unit circle about (0,0) . Evidently no other circle with the same centre can contain both (0, 0) and (NT2,IT/4) . An X can also be constructed by adjoining to the o above set the point (2 sinTr/12, TT/12) .
122388919
Enumeration of quadrangular dissections of the disk
124806549
Sur les ensembles de sommets indépendants dans les graphes chromatiques minimaux
116788453
On an open problem of Paul Turán concerning 3-graphs
The third of Paul Turan’s 1961 list of Research Problems [4] reads: 
“If 2 ≦ l < k < n, then what is the minimal number μ of combinations C 1,C 2,..., C μ taken l at a time out of 1, 2,..., n with the property that each combination taken k at a time out of 1, 2,..., n contains at least one C j ? (For l = 2 the question is settled with exhibiting the only minimal C-system in my paper “Egy grafelmeleti szelsőertek-feladatrol”, Mat. es Fiz. Lapok (1941) 436–451, in Hungarian with German abstract.)”
121690558
On a hierarchy of generalized diagonal dominance properties for complex matrices
ABSTRACT. This article concerns dominance conditions for an nXm matrix. In the simplest kind of dominance, the (absolute) value of the diagonal element exceeds the sum of the absolute values of the nondiagonal elements on the same row. This condition has been generalized in the literature in several ways, of which we consider ways in which the rows of the matrix cooperate. Our work amounts to a sorting out of certain dominance conditions that belong to a class e of dominance conditions. We prove a theorem characterizing all true statements of the form
123473446
Hesse's theorem for a quadrilateral whose sides touch a conic