7654369
Extension of a list coloring problem
Abstract For a graph H , f ( H ) is the smallest integer k such that the join of H with an empty graph E k of order k is not | V ( H ) | -choosable. It was conjectured that for a triangle-free graph G , f ( G ) = n 2 μ ( G ) n n − 2 μ ( G ) , where n = | V ( G ) | and μ ( G ) is the cardinality of a maximum matching of graph G [S. Gravier, F. Maffray, B. Mohar, On a list-coloring problem, Discrete Math. 268 (2003) 303–308]. We verify this conjecture in the case of forests, and propose some related problems.
9614158
Edge choosability of planar graphs without small cycles
Abstract We investigate structural properties of planar graphs without triangles or without 4-cycles, and show that every triangle-free planar graph G is edge-( Δ ( G )+1)-choosable and that every planar graph with Δ ( G )≠5 and without 4-cycles is also edge-( Δ ( G )+1)-choosable.
205935860
An ATM cross-connecting node using optical CDMA
An asynchronous transfer mode (ATM) cross-connecting node is proposed based on direct sequence optical code division multiple access (DS-OCDMA). No buffering is necessary to facilitate switching because code conversion is instead emulating the switching function. The switch is also capable of limited dynamic bandwidth allocation. It is free from timing jitters and switching delay is significantly reduced. The switch provides a new approach to asynchronous cross-connection in the ATM core network, locally or over a wider area. The performance with the new proposed switch is evaluated using prime and modified prime OCDMA codes.
32712531
Some properties of 3-domination-critical graphs
Abstract A graph G is 3- γ -critical if its domination number γ is 3 and the addition of any edge decreases γ by 1. Wojcicka conjectured that every 3- γ -critical graph with minimum degree δ ⩾2 has a hamiltonian cycle. In this paper, we prove that if G is a 3- γ -critical connected graph of order n with minimum degree δ ⩾2, then (1) G is 1-tough; (2) the circumference of G is at least n −1.
205876162
Independence and connectivity in 3-domination-critical graphs
Let δ, γ, κ and α be, respectively, the minimum degree, the domination number, the con nectivity and the independence number of a graph G. The graph G is 3-domination-critical if γ = 3 and the addition of any edge decreases γ by 1. In this paper, we prove that if G is a 3-domination-critical graph, then α ≤ κ + 2; and moreover, if κ ≤ δ -1, then α ≤ κ + 1. We also give a short proof of Wojcicka's result, which says that every connected 3-domination-critical graph of order at least 7 contains a hamiltonian path (J. Graph Theory 14 (1990) 205).
1918361
Canny edge detection enhancement by scale multiplication
The technique of scale multiplication is analyzed in the framework of Canny edge detection. A scale multiplication function is defined as the product of the responses of the detection filter at two scales. Edge maps are constructed as the local maxima by thresholding the scale multiplication results. The detection and localization criteria of the scale multiplication are derived. At a small loss in the detection criterion, the localization criterion can be much improved by scale multiplication. The product of the two criteria for scale multiplication is greater than that for a single scale, which leads to better edge detection performance. Experimental results are presented.
12223354
Disjoint NP-pairs
We study the question of whether the class DisNP of disjoint pairs (A, B) of NP-sets contains a complete pair. The question relates to the question of whether optimal proof systems exist, and we relate it to the previously studied question of whether there exists a disjoint pair of NP-sets that is NP-hard. We show under reasonable hypotheses that nonsymmetric disjoint NP-pairs exist, which provide additional evidence for the existence of P-inseparable disjoint NP-pairs. We construct an oracle relative to which the class of disjoint NP-pairs does not have a complete pair, an oracle relative to which optimal proof systems exist, hence complete pairs exist, but no pair is NP-hard, and an oracle relative to which complete pairs exist, but optimal proof systems do not exist.