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A graph is 1-planar if it can be embedded in the plane so that each edge is crossed by at most one other edge. We prove that each 1-planar graph of minimum degree 5 and girth 4 contains (1) a 5-vertex adjacent to an ≤ 6-vertex, (2) a 4-cycle whose every vertex has degree at most 9, (3) a K 1,4 with all vertices having degree at most 11.

A graph is called 1-planar if it can be drawn in the plane so that each of its edges is crossed by at most one other edge. We show that every 1-planar drawing of any 1-planar graph on n vertices has at most n − 2 crossings; moreover, this bound is tight. By this novel necessary condition for 1-planarity, we characterize the 1-planarity of Cartesian product… (More)

The effects of humor on increasing discomfort thresholds were tested with Transcutaneous End Nerve Stimulation (TENS). Undergraduate students (n = 31) with high or low scores on Martin and Lecourt's Situational Humor Questionnaire were randomly assigned to a humor or nonhumor condition. Discomfort thresholds for TENS were assessed before and during… (More)

- W. A. Petersen, D. Hudak, V. N. Bringi, P. Siqueira, A. Tokay, V. Chandrasekar +6 others
- 2007

- G. A. Isaac, J. K. Ayers, M. Bailey, L. Bissonnette, B. C. Bernstein, S. G. Cober +19 others
- 2005

with the main center of interest being near Mirabel, Quebec. The AIRS II project operational objectives are to: a) develop techniques/systems to remotely detect, diagnose and forecast hazardous winter conditions at airports, b) improve weather forecasts of aircraft icing conditions, c) better characterize the aircraft-icing environment and d) improve our… (More)

A graph is called 1-planar if there exists a drawing in the plane so that each edge contains at most one crossing. We study maximal 1-planar graphs from the point of view of properties of their diagrams, local structure and hamiltonicity.