Now showing items 1-3 of 3
Small triangle-free configurations of points and lines
In this paper we show that all combinatorial triangle-free configurations (v_3) for v (is less than or equal to) 8 are geometrically realizable. We also show that there is a unique smallest astral (18_3) triangle-free configuration, and its Levi graph is the generalized Petersen graph G(18, 5). In addition, we present geometric ...
Configurations of points and lines
A vigorous study of geometric configurations started in the 1870's but was essentially abandoned early in the twentieth century. New approaches found during the last two decades prompted a renewed interest in the topic, heightened by the discovery that many of the results of early investigations were invalid as stated and ...
3-connected configurations (n3) with no Hamiltonian circuit
For more than a century there have been examples of (n3) configurations without a Hamiltonian circuit. However, all these examples were only 2-connected. It has been believed that all geometric 3-connected configurations (n3) admit Hamiltonian circuits. We present a 3-connected configuration (253) of points and lines in the ...