On Edge-Disjoint Pairs Of Matchings

For a graph G, consider the pairs of edge-disjoint matchings whose union consists of as many edges as possible. Let H be the largest matching among such pairs. Let M be a maximum matching of G. We show that 5/4 is a tight upper bound for |M|/|H|.Comment: 8 pages, 2 figures, Submitted to Discrete Mathematic

Cubic interactions of massless bosonic fields in three dimensions

Parity-even cubic vertices of massless bosons of arbitrary spins in three dimensional Minkowski space are classified in the metric-like formulation. As opposed to higher dimensions, there is at most one vertex for any given triple $s_1,s_2,s_3$ in three dimensions. All the vertices with more than three derivatives are of the type $(s,0,0)$, $(s,1,1)$ and $(s,1,0)$ involving scalar and/or Maxwell fields. All other vertices contain two (three) derivatives, when the sum of the spins is even (odd). Minimal coupling to gravity, $(s,s,2)$, has two derivatives and is universal for all spins (equivalence principle holds). Minimal coupling to Maxwell field, $(s,s,1)$, distinguishes spins $s\leq 1$ and $s\geq 2$ as it involves one derivative in the former case and three derivatives in the latter case. Some consequences of this classification are discussed.Comment: 18 page

IMPACT OF REGULATED PRICE ADJUSTMENTS ON PRICE VARIABILITY IN A VERY LOW INFLATION TRANSITION ECONOMY: CASE OF ARMENIA

The impact of macroeconomic management (monetary policy) and administrative price adjustments on price variability in a low inflation economy characterized by relatively frequent administrative price adjustments is examined. Fluctuations of market determined prices, prices of agricultural goods in particular, are linked to the lack of synchronization between administrative price changes and monetary policy. If monetary policy does not account for expected changes in administrative prices, demand in “free” goods markets will shift causing fluctuation of prices for agricultural goods, because the supply of these goods is highly inelastic in Armenia. The findings contribute to a better understanding of agricultural price variability during 1998-2002. The impact of macroeconomic policy and structural adjustments on income distribution and rural poverty incidence are also examined. This research has immediate policy implications since Armenia will undergo major upward price adjustments for goods and services with regulated prices, which may have a negative impact on income distribution if aggregate demand management is unchanged.http://deepblue.lib.umich.edu/bitstream/2027.42/40117/3/wp731.pd

On disjoint matchings in cubic graphs

For $i=2,3$ and a cubic graph $G$ let $\nu_{i}(G)$ denote the maximum number of edges that can be covered by $i$ matchings. We show that $\nu_{2}(G)\geq {4/5}| V(G)|$ and $\nu_{3}(G)\geq {7/6}| V(G)|$. Moreover, it turns out that $\nu_{2}(G)\leq \frac{|V(G)|+2\nu_{3}(G)}{4}$.Comment: 41 pages, 8 figures, minor chage

Measures of edge-uncolorability

The resistance $r(G)$ of a graph $G$ is the minimum number of edges that have to be removed from $G$ to obtain a graph which is $\Delta(G)$-edge-colorable. The paper relates the resistance to other parameters that measure how far is a graph from being $\Delta$-edge-colorable. The first part considers regular graphs and the relation of the resistance to structural properties in terms of 2-factors. The second part studies general (multi-) graphs $G$. Let $r_v(G)$ be the minimum number of vertices that have to be removed from $G$ to obtain a class 1 graph. We show that $\frac{r(G)}{r_v(G)} \leq \lfloor \frac{\Delta(G)}{2} \rfloor$, and that this bound is best possible.Comment: 9 page