Wavefront and caustic surfaces of refractive laser beam shaper
David L. Shealy, John A. Hoffnagle
SPIE Optical Engineering + Applications 2007
A set of vertices X is called irredundant if for every x in X the closed neighborhood N[x] contains a vertex which is not a member of N[X-x], the union of the closed neighborhoods of the other vertices. In this paper we show that for circular arc graphs the size of the maximum irredundant set equals the size of a maximum independent set. Variants of irredundancy called oo-irredundance, co-irredundance, and oc-irredundancy are defined using combinations of open and closed neighborhoods. We prove that for circular arc graphs the size of a maximum oo-irredundant set equals 2β* or 2β*+1 (depending on parity) where β* is the strong matching number. We also show that for circular arc graphs, the size of a maximum co-irredundant set equals the maximum number of vertices in a set consisting of disjoint K1's and K2's. Similar results are proven for bipartite graphs. © 1993.
David L. Shealy, John A. Hoffnagle
SPIE Optical Engineering + Applications 2007
Michael Ray, Yves C. Martin
Proceedings of SPIE - The International Society for Optical Engineering
Sankar Basu
Journal of the Franklin Institute
Hang-Yip Liu, Steffen Schulze, et al.
Proceedings of SPIE - The International Society for Optical Engineering