Finite 33-connected homogeneous graphs

A finite graph \G is said to be {\em $(G,3)$-$($connected$)$ homogeneous} if every isomorphism between any two isomorphic (connected) subgraphs of order at most $3$ extends to an automorphism $g\in G$ of the graph, where $G$ is a group of automorphisms of the graph. In 1985, Cameron and Macpherson determined all finite $(G, 3)$-homogeneous graphs. In this paper, we develop a method for characterising $(G,3)$-connected homogeneous graphs. It is shown that for a finite $(G,3)$-connected homogeneous graph \G=(V, E), either G_v^{\G(v)} is $2$--transitive or G_v^{\G(v)} is of rank $3$ and \G has girth $3$, and that the class of finite $(G,3)$-connected homogeneous graphs is closed under taking normal quotients. This leads us to study graphs where $G$ is quasiprimitive on $V$. We determine the possible quasiprimitive types for $G$ in this case and give new constructions of examples for some possible types

How does fiscal decentralization affect aggregate, national, and subnational government size?

Beyond conducting the usual regression analysis of the relationship between fiscal decentralization and aggregate government size (national and subnational combined), this paper makes the first attempt to examine how different fiscal decentralization measures affect the sizes of national and subnational (state and local combined) governments. An econometric analysis using panel data from 32 industrial and developing countries, 1980¨C1994, finds that (1) expenditure decentralization leads to smaller national governments, larger subnational governments, and larger aggregate governments; (2) revenue decentralization increases subnational governments by less than it reduces national governments, hence leads to smaller aggregate governments; and (3) vertical imbalance tends to increase the sizes of subnational, national, and aggregate governments.Fiscal decentralization, Size of government, Vertical imbalance, Borrowing constraints

Fiscal decentralization, revenue and expenditure assignments, and growth in China

Theory suggests that a close match between revenue and expenditure assignments at sub-national levels benefits allocative efficiency, and hence economic growth. That is, a convergence of revenue and expenditure assignments at sub-national levels of government should, according to the theory, be positively associated with a higher growth rate. In the case of China, this paper shows, divergence, rather than convergence, in revenue and expenditures at the sub-national level of government is associated with higher rates of growth. A panel dataset for 30 provinces in China is used to examine the relationship between fiscal decentralization and economic growth over two phases of fiscal decentralization in China: (1) 1979¨C1993 under the fiscal contract system, and (2) 1994¨C1999 under the tax assignment system. The seeming contradiction between the theory and evidence in the China case is reconciled by taking into account the institutional arrangements that prevailed during the two phases of fiscal decentralization, in particular the inconsistency between the assumptions of the theory of fiscal decentralization and the institutional reality of China.Fiscal decentralization, Economic growth, Revenue, Expenditure

Holographic Algorithm with Matchgates Is Universal for Planar #\#CSP Over Boolean Domain

We prove a complexity classification theorem that classifies all counting constraint satisfaction problems ($\#$CSP) over Boolean variables into exactly three categories: (1) Polynomial-time tractable; (2) $\#$P-hard for general instances, but solvable in polynomial-time over planar graphs; and (3) $\#$P-hard over planar graphs. The classification applies to all sets of local, not necessarily symmetric, constraint functions on Boolean variables that take complex values. It is shown that Valiant's holographic algorithm with matchgates is a universal strategy for all problems in category (2).Comment: 94 page