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|Title: ||The cone of balanced subgraphs|
|Authors: ||BHATTACHARYA, A|
|Issue Date: ||2009|
|Publisher: ||ELSEVIER SCIENCE INC|
|Citation: ||LINEAR ALGEBRA AND ITS APPLICATIONS, 431(1-2), 266-273|
|Abstract: ||In this paper we study a 2-color analog of the cycle cone of a graph. Suppose the edges of a graph are colored red and blue. A nonnegative real vector on the edges is said to be balanced if the red sum equals the blue sum at every vertex. A balanced subgraph is a subgraph whose characteristic vector is balanced (i.e., red degree equals blue degree at every vertex). By a sum (respectively, fractional sum) of cycles we mean a nonnegative integral (respectively, nonnegative rational) combination of characteristic vectors of cycles. Similarly, we define sum and fractional sum of balanced subgraphs. We show that a balanced sum of cycles is a fractional sum of balanced subgraphs. (C) 2009|
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