An edge-coloring of a graph G is said to be odd if for each vertex v of G and each color c, the vertex v either uses the color c an odd number of times or does not use it at all. The minimum number of colors needed for an odd edge-coloring of G is the odd chromatic index χ o (G). These notions were introduced by Pyber in [7], who showed that 4 colors suffice for an odd edge-coloring of any simple graph. In this paper, we consider loopless subcubic graphs, and give a complete characterization in terms of the value of their odd chromatic index.
We consider a finite, aspherical, 2-dimensional Cohen-Macaulay simplicial complex and we find additional conditions that imply the universal cover z has one end. In order to find these additional conditions we use a form of "Zeeman Duality". The context is an attempt to better understand duality groups.
We will discuss the effectiveness of online homework in Calculus courses. Specifically, we will discuss the use of WeBWorK -an open-source online homework system supported by the Mathematical Association of America and the National Science Foundation. We will confer practices for implementing WeBWorK homework for Calculus and discuss student learning using this online homework system.2010 Mathematics Subject Classification. 97U70.
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