The main contributions of this paper are three-fold. First, we use a dynamic approach based on Reiter’s pioneering work on Karp-Miller computation graphs [19] to give a new and short proof of Mohar’s Minty-type Theorem [15]. Second, we bridge circular colorings and discrete event dynamic systems to show that the Barbosa and Gafni’s results on circular chromatic number [5, 21] can be generalized...

In this paper, we consider the circular chromatic number c (G) of series-parallel graphs G. It is well known that series-parallel graphs have chromatic number at most 3. Hence their circular chromatic number is also at most 3. If a series-parallel graph G contains a triangle , then both the chromatic number and the circular chromatic number of G are indeed equal to 3. We shall show that if a se...

For an integer k > 0, a graph G is k-triangular if every edge of G lies in at least k distinct 3-cycles of G. In [J. Graph Theory, 11 (1987), 399-407], Broersma and Veldman proposed an open problem: For a given positive integer k, determine the value s for which the statement Let G be a k-triangular graph. Then L(G), the line graph of G, is s-hamiltonian if and only L(G) is (s + 2)-connected is...