The odd-even invariant for graphs - Eager, Richard; Lawrence, Jim (European journal of combinatorics, 2015)
The odd-even invariant for graphs is the graphic version of the odd-even invariant for oriented matroids. Here, simple properties of this invariant are verified, and for certain graphs, including chordal graphs and complete bipartite graphs, its value is determined. The odd-even chromatic polynomial is introduced, its coefficients are briefly studied, and it is shown that the absolute value of this polynomial at −1 equals the odd-even invariant, in analogy with the usual chromatic polynomial and the number of acyclic orientations.
Available online: 25 April 2015
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