Implementing balanced and restorative justice : victim, offender, community : a guide for law enforcement officers /

This publication is one in a series of guides designed to assist in the statewide promotion of balanced and restorative justice. BARJ is a philosophy of justice that can guide the work of individuals who deal with juvenile offenders, their victims, and the communities in which they live.

Implementing balanced and restorative justice : victim, offender, community : a guide for juvenile detention /

This publication is one in a series of guides designed to assist in the statewide promotion of balanced and restorative justice. BARJ is a philosophy of justice that can guide the work of individuals who deal with juvenile offenders, their victims, and the communities in which they live.

Operator, organizational, and intermediate (direct support and general support) maintenance manual ... : switch, balanced magnetic SA-1955 ()/FSS-9(V) NSN 6350-00-228-2500.

"24 July 1974."

Budget reductions for FY 1986 : Balanced Budget and Emergency Deficit Control Act of 1985 : report to the President and Congress /

"B-221498"--P. 1.

North Carolina's balanced growth strategy /

"HUD-PDR-644-5"-- P. 4 of cover.

Balanced budget requirements : state experiences and implications for the federal government : briefing report to the Chairman, Committee on the Budget, House of Representatives /

148877GAO (202) 512-6000 (Voice); (301) 258-4066 (Fax)

The White House Conference on Balanced National Growth & Economic Development : final report, July 1978.

Includes bibliographies and indexes.

Signal flow graphs and applications /

Bibliography: p. 207-210.

Decompositions of complete tripartite graphs into triangles with an edge attached

Let K(r, s, t) denote the complete tripartite graph with partite sets of size r, s and t, where r less than or equal to s less than or equal to t. Let D be the graph consisting of a triangle with an edge attached. We show that K(r, s, t) may be decomposed into copies of D if and only if 4 divides rs + st + rt and t less than or equal to 3rs/(r + s).

Balanced critical sets in Latin squares

In this note we first introduce balanced critical sets and near balanced critical sets in Latin squares. Then we prove that there exist balanced critical sets in the back circulant Latin squares of order 3n for n even. Using this result we decompose the back circulant Latin squares of order 3n, n even, into three isotopic and disjoint balanced critical sets each of size 3n. We also find near balanced critical sets in the back circulant Latin squares of order 3n for n odd. Finally, we examine representatives of each main class of Latin squares of order up to six in order to determine which main classes contain balanced or near balanced critical sets.

Common multiples of complete graphs and a 4-cycle

A graph G is a common multiple of two graphs H-1 and H-2 if there exists a decomposition of G into edge-disjoint copies of H-1 and also a decomposition of G into edge-disjoint copies of H-2. In this paper, we consider the case where H-1 is the 4-cycle C-4 and H-2 is the complete graph with n vertices K-n. We determine, for all positive integers n, the set of integers q for which there exists a common multiple of C-4 and K-n having precisely q edges. (C) 2003 Elsevier B.V. All rights reserved.

Cube factorizations of complete graphs

A cube factorization of the complete graph on n vertices, K-n, is a 3-factorization of & in which the components of each factor are cubes. We show that there exists a cube factorization of & if and only if n equivalent to 16 (mod 24), thus providing a new family of uniform 3 -factorizations as well as a partial solution to an open problem posed by Kotzig in 1979. (C) 2004 Wiley Periodicals, Inc.

On the forced matching numbers of bipartite graphs

Let G be a graph that admits a perfect matching. A forcing set for a perfect matching M of G is a subset S of M, such that S is contained in no other perfect matching of G. This notion has arisen in the study of finding resonance structures of a given molecule in chemistry. Similar concepts have been studied for block designs and graph colorings under the name defining set, and for Latin squares under the name critical set. There is some study of forcing sets of hexagonal systems in the context of chemistry, but only a few other classes of graphs have been considered. For the hypercubes Q(n), it turns out to be a very interesting notion which includes many challenging problems. In this paper we study the computational complexity of finding the forcing number of graphs, and we give some results on the possible values of forcing number for different matchings of the hypercube Q(n). Also we show an application to critical sets in back circulant Latin rectangles. (C) 2003 Elsevier B.V. All rights reserved.

Decompositions of complete graphs into triangles and Hamilton cycles

For all odd integers n greater than or equal to 1, let G(n) denote the complete graph of order n, and for all even integers n greater than or equal to 2 let G,, denote the complete graph of order n with the edges of a 1-factor removed. It is shown that for all non-negative integers h and t and all positive integers n, G, can be decomposed into h Hamilton cycles and t triangles if and only if nh + 3t is the number of edges in G(n). (C) 2004 Wiley Periodicals, Inc.