John Seamons

The Geometric Thickness of K13 Is Three: An Exact Integer-Coordinate Witness

The geometric thickness of a graph is the minimum number of plane straight-line layers whose union is the graph, with one common placement of the vertices. Dillencourt, Eppstein and Hirschberg left the exact values for K13 and K14 open. We give 13 integer points and a partition o...

The Geometric Thickness of K13 Is Three: An Exact Integer-Coordinate Witness

The geometric thickness of a graph is the minimum number of plane straight-line layers whose union is the graph, with one common placement of the vertices. Dillencourt, Eppstein and Hirschberg left the exact values for K13 and K14 open. We give 13 integer points and a partition o...

AN EXACT RATIONAL COUNTEREXAMPLE TO ERDŐS'S SQUARE-PACKING CONJECTURE f(k²+1)=k (PROBLEM #106)

This preprint gives an explicit exact rational counterexample to Erdős's square-packing conjecture f(k²+1)=k, catalogued as Erdős Problem #106. The primary-source formulation of Erdős and Graham (1975) uses total circumference instead: if F_EG(n) is the maximum total circumferenc...

AN EXACT RATIONAL COUNTEREXAMPLE TO ERDŐS'S SQUARE-PACKING CONJECTURE f(k²+1)=k (PROBLEM #106)

This preprint gives an explicit exact rational counterexample to Erdős's square-packing conjecture f(k²+1)=k, catalogued as Erdős Problem #106. The primary-source formulation of Erdős and Graham (1975) uses total circumference instead: if F_EG(n) is the maximum total circumferenc...