Acyclic Edge Coloring of Graphs with Maximum Degree 4

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a'(G). It was conjectured by Alon, Sudakov, and Zaks that for any simple and finite graph G, a'(G) <= Delta+2, where Delta=Delta(G) denotes the maximum degree of G. We prove the conjecture for connected graphs with Delta(G)<= 4, with the additional restriction that m <= 2n-1, where n is the number of vertices and m is the number of edges in G. Note that for any graph G, m <= 2n, when Delta(G)<= 4. It follows that for any graph G if Delta(G)<= 4, then a'(G) <= 7.

Enhancing human action recognition with region proposals

Deep convolutional network models have dominated recent work in human action recognition as well as image classification. However, these methods are often unduly influenced by the image background, learning and exploiting the presence of cues in typical computer vision datasets. For unbiased robotics applications, the degree of variation and novelty in action backgrounds is far greater than in computer vision datasets. To address this challenge, we propose an “action region proposal” method that, informed by optical flow, extracts image regions likely to contain actions for input into the network both during training and testing. In a range of experiments, we demonstrate that manually segmenting the background is not enough; but through active action region proposals during training and testing, state-of-the-art or better performance can be achieved on individual spatial and temporal video components. Finally, we show by focusing attention through action region proposals, we can further improve upon the existing state-of-the-art in spatio-temporally fused action recognition performance.