Marking Games and the Oriented Game Chromatic Number of Partial <Emphasis Type="Italic">k</Emphasis>-Trees

 Nešetřil and Sopena introduced the concept of oriented game chromatic number. They asked whether the oriented game chromatic number of partial k-trees was bounded. Here we answer their question positively. Received: January 12, 2001 Final version received: February 25, 2002     

Faddeev-Noble Versus Sasakawa-Sawada Equations for the Nuclear Three-Body Coulomb Problem

We compare the efficiency of two Faddeev-type approaches for the nuclear three-body Coulomb problem. The first one is a modification of Noble’s approach, the second one is due to Sasakawa and Sawada. In an integral-equation formulation both of these methods rely on the same Green’s operators and driving terms. The differences lie in the treatment of the long-range Coulomb potentials. Numerical examples show that the modified Faddeev-Noble approach provides for faster convergence.     

On-line arbitrarily vertex decomposable trees

A tree T is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to the order of T there is a sequence of vertex-disjoint subtrees of T whose orders are given by τ. An on-line version of the problem of characterizing arbitrarily vertex decomposable trees is completely solved here.     

Degree Sums and Covering Cycles

It is shown that if in a simple graph G of order n the sum of degrees of any three pairwise non-adjacent vertices is at least n, then there are two cycles (or one cycle and an edge or a vertex) of GF that contain all the vertices. © 1995 John Wiley & Sons, Inc.     

Contractions and minimalk-colorability

Coloring the vertex set of a graphG with positive integers, thechromatic sum (G) ofG is the minimum sum of colors in a proper coloring. Thestrength ofG is the largest integer that occurs in every coloring whose total is(G). Proving a conjecture of Kubicka and Schwenk, we show that every tree of strengths has at least ((2 + ) ^s–1 – (2 – ) ^s–1)/ vertices (s 2). Surprisingly, this extremal result follows from a topological property of trees. Namely, for everys 3 there exist precisely two treesT _s andR _s such that every tree of strength at leasts is edge-contractible toT _s orR _s .     

Sub-Ramsey numbers for arithmetic progressions

Letm 3 andk 1 be two given integers. Asub-k-coloring of [n] = {1, 2,...,n} is an assignment of colors to the numbers of [n] in which each color is used at mostk times. Call an arainbow set if no two of its elements have the same color. Thesub-k-Ramsey number sr(m, k) is defined as the minimumn such that every sub-k-coloring of [n] contains a rainbow arithmetic progression ofm terms. We prove that((k – 1)m ²/logmk) sr(m, k) O((k – 1)m ² logmk) asm , and apply the same method to improve a previously known upper bound for a problem concerning mappings from [n] to [n] without fixed points.Research supported in part by Allon Fellowship and by a Bat Sheva de-Rothschild grant.Research supported in part by the AKA Research Fund of the Hungarian Academy of Sciences, grant No. 1-3-86-264.     

Positron annihilation and1H NMR study of [Zn(1-propyltetrzole)6](BF4)2 and [Fe(Methyltetrazole)6](BF4)2 complexes

The complexes [Zn(1-propyltetraole)₆](BF₄)₂ (Zn-ptz) and [Fe(methyltetrazole)₆](BF₄)₂ (Fe-mtz) were investigated by positron annihilation and solid-state NMR spectroscopy. For Zn-ptz signs of structural rearrangements were found between 70 and 145 K. For the spin-crossover complex Fe-mtz a transition affecting the high-spin stat Fe²⁺ ions at lattice site B occurs below 15 K.     

The Ru(dipy)32+-Bromate-Malonic acid oscillating system

The Ru(dipy) ₃ ²⁺ -bromate-malonic acid oscillating system was in vestigated. It has been established that at early stages of the reaction the period of oscillation is about 20 sec and the potential change is about 170 mV; chloride at concentrations hiherg than 10^–3M is an inhibitor. The rates of both heat evolution and formation of bromomalonic acid are periodic. The activation energy of the oscillating (E) is 16.2 kcal mol^–1. Ru(dipy) ₃ ²⁺ -- . , 20 , 170 ; , - 10^–3 M, . . (E) 16,2 /.