March 25, 2005 14:14 WSPC/Guidelines Chordsep
e a boolean expression in conjunctive normal form with nvariables and m clauses such that each clause has three literals. Let GExp be thegraph (V, E), where V consists of the variables and clauses of Exp(x), and (xi , cj ) E if and only if variable xi occurs in clause cj . If GExp is planar, then decidingwhether there is a assignment of true and false values for x such that Exp(x) istrue is known as the planar 3SAT problem. If we also require that each clause hasexactly one true literal, the problem is known as planar 1-in-3SAT. Laroche 11proved that planar 1-in-3SAT is NP-complete. We prove our theorem by describinga polynomial-time reduction from this problem.We first show how to create a polygon P and a set of blue and red points froma planar embedding of the graph GExp . Figure 6 shows the encoding of a variable. We imagine that the boundary of the variable gadget is oriented clockwise.The inside of the variable is the connected portion of the boundary that bounds ahole; the remainder of the boundary is the outside. There are exactly two minimalsets of chords that separate the blue and red points within each variable gadget;these correspond to assigning the values true and false to the variable. The truesetting consists of chords that from the inside of the variable gadget go in clockwise direction acr
JEFF ERICKSON Department of Computer Science, University of Illinois at Urbana-Champaign, 1304 W. Springfield Avenue, Urbana, IL 61801, USA. jeffe@cs.uiuc.edu FERRAN HURTADO Departement de Matem atica Aplicada II, Universitat Polit ecnica de Catalunya, Pau Gargallo 5,
Chevy Silverado 1999-2005, Chevy Suburban 2000-2005, Chevy Tahoe 2000-2005, Cadillac Escalade 2002-2005, Cadillac Escalade EXT 2002-2005, GMC Sierra 1999-2005, GMC Yukon XL 2000-2005, GMC Yukon Denali 2001-2005, Chevy Avalanche 2002-2005 THE safety accessory of the 21st Century.
KENWOOD TS-940 PAGE Version 2: 4 April 2005, Version 3: 25 April 2005, Version 4: 27 May 2005, Version 5: 31May 2005, Version 6: 10 June 2005: Version 7: 16 June 2005: Version 8: 25 July 2005Version 9: 30 July 2005. Version 10: 4 August 2005, Version 11: 13 Sep 2005, Version 12: 18 October 2005, Version 13: 23 October 2005,
Sugar Camp Creek Wetland Compensation Site September 1, 2004 to September 20, 2005 Water-Level Elevations at Monitoring Instruments Located on the East Side of Sugar Camp Creek 122.5 123.0 123.5 124.0 124.5 Aug 2004 Sep 2004 Oct 2004 Nov 2004 Dec 2004 Jan 2005 Feb 2005 Mar 2005 Apr 2005 May 2005 Jun 2005 Jul 2005 Aug 2005 Sep 2005 Oct 2005
US 7.689,548 B2 Page 2 2005/0O862O6 2005/0091111 2005.0102270 2005/O137939 2005, 014.4065 2005/0171932 2005/0222901 2005/0228797 2005/0262428
Important Days in March March 1 -Zero Discrimination Day March 3 -World Wildlife Day; National Defence Day March 4 -National Security Day March 8 -International Women's Day March 13 -No Smoking Day (Second Wednesday in March) March 15 -World Disabled Day; World Consumer Rights Day March 18 -Ordnance Factories Day (India) March 21 -World Down Syndrome Day; World Forestry Day
HB-212 5/19/2005 161 Third Reading HB-212 5/19/2005 166 Vote Intention HB-213 2/24/2005 20 First Reading HB-215 2/24/2005 19 First Reading HB-215 5/4/2005 14 Second Reading HB-215 5/17/2005 28 Recalled HB-215 5/19/2005 167 Third Reading HB-220 4/14/2005 7 First Reading .
kc-2005-0827 melissa rollings v nationwide insurance 9/22/2005 0:00 kc-2005-0828 asset acceptance llc v cheryl holliday 9/22/2005 0:00 kc-2005-0831 kelly mcneil v michelle martin 9/22/2005 0:00 kc-2005-0833a susan brown v camelia albright 9/23/2005 0:00 kc
Schiavo ex rel. Schiavo, _ F.3d _, 2005 WL 648897 (11th Cir. Mar. 23, 2005) (Schiavo I), stay denied, _ S. Ct. _, 2005 WL 672685 (Mar. 24, 2005). After that appeal was taken, the plaintiffs filed an amended complaint on March 22, 2005, adding four more counts, and a second amended complaint on March 24, 2005, adding a fifth count. On the basis of the claims contained in those new .
