Local approximations for maximum partial subgraph problem

We deal with MAXH₀-FREE PARTIAL SUBGRAPH. We mainly prove that 3-locally optimum solutions achieve approximation ratio (δ₀+1)/(B+2+ν₀), where B=max_v∈Vd_G(v), δ₀=min_v∈V(H0)d_H0(v) and ν₀=(|V(H₀)|+1)/δ₀. Next, we show that this ratio rises up to 3/(B+1) when H₀=K₃. Finally, we provide hardness results for MAXK₃-FREE PARTIAL SUBGRAPH.     

2‐connected 7‐coverings of 3‐connected graphs on surfaces

An m‐covering of a graph G is a spanning subgraph of G with maximum degree at most m. In this paper, we shall show that every 3‐connected graph on a surface with Euler genus k ≥ 2 with sufficiently large representativity has a 2‐connected 7‐covering with at most 6k ? 12 vertices of degree 7. We also construct, for every surface F² with Euler genus k ≥ 2, a 3‐connected graph G on F² with arbitrarily large representativity each of whose 2‐connected 7‐coverings contains at least 6k ? 12 vertices of degree 7. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 26–36, 2003     

最大2-正则诱导子图的长度

设G是2-连通图，c(G)是图G的最长诱导圈的长度，c′(G)是图G的最长诱导2-正则子图的长度。本文我们用图的特征值给出了c(G)和c′(G)的几个上界。     

关于k—消去图的若干新结果

设G是一个图．k是自然数．图G的一个k-正则支撑子图称为G的一个k-因子．若对于G的每条边e．G—e都存在一个k-因子，则称G是一个k-消去图．该文得到了一个图是k-消去图的若干充分条件，推广了文［2—4］中有关结论．     

Odd subgraphs and matchings

Let G be a graph and f : V(G)→{1,3,5,…}. Then a subgraph H of G is called a (1,f)-odd subgraph if deg_H(x){1,3,…,f(x)} for all xV(H). If f(x)=1 for all xV(G), then a (1,f)-odd subgraph is nothing but a matching. A (1,f)-odd subgraph H of G is said to be maximum if G has no (1,f)-odd subgraph K such that |K|>|H|. We show that (1,f)-odd subgraphs have some properties similar to those of matchings, in particular, we give a formula for the order of a maximum (1,f)-odd subgraph, which is similar to that for the order of a maximum matching.     

Estimations of subgraph positions in molecular graphs and their common subgraph peculiarities

Some questions emerged from electronic data processing of molecular structures (graphs) and its fragments have been considered in this work. Quantitative estimations of subgraph positions in molecular graphs are presented and some properties of their maximal common subgraphs are described.     

The polynomial reconstruction problem: The first 50 years

The problem of reconstructing the characteristic polynomial of a graph of order at least 3 from the collection of characteristic polynomials of its vertex-deleted subgraphs was posed by Cvetkovi? in 1973 as a spectral counter part to the well-known Ulam's reconstruction conjecture. Over the last 50 years, this problem has received notable attention, many positive results have been obtained, but in the general case the problem is still unresolved. In particular, no counter example is found in literature. In this expository paper we survey classical and some more recent results concerning the polynomial reconstruction problem, discuss some related problems, variations and generalizations.     

Accelerating the calculations of binary detour phase method by integrating both CUDA and Matlab programming for GPU's parallel computations

The availability of state of art GPGPU cards can play a promising role in accelerating the calculations of computer generated holograms (CGH) where one of the main problems of generating such holograms is the need for massive amount of calculations. Both CUDA and Matlab can be used alone to fulfill this purpose but using both at the same time gives a number of benefits. This paper is dedicated to present a performance study of applying Fermi-Architecture CUDA-enabled GPGPU card for speeding up the calculations of binary detour phase holograms using both Matlab and CUDA programming.