A note on circular colorings of edge-weighted digraphs

Wu Hsiung Lin, Hong Gwa Yeh

研究成果: 雜誌貢獻期刊論文同行評審


An edge-weighted digraph (G, ℓ) is a strict digraph G together with a function ℓ assigning a real weight ℓuv to each arc uv. (G, ℓ) is symmetric if uv is an arc implies that so is vu. A circular r-coloring of (G, ℓ) is a function φ assigning each vertex of G a point on a circle of perimeter r such that, for each arc uv of G, the length of the arc from φ(u) to φ(v) in the clockwise direction is at least ℓuv. The circular chromatic number χc(G, ℓ) of (G, ℓ) is the infimum of real numbers r such that (G, ℓ) has a circular r-coloring. Suppose that (G, ℓ) is an edge-weighted symmetric digraph with positive weights on the arcs. Let T be a {0, 1}-function on the arcs of G with the property that T(uv) + T(vu) = 1 for each arc uv in G. In this note we show that if, for each dicycle C of G satisfying, then (G, ℓ) has a circular r-coloring.

頁(從 - 到)2159-2167
期刊Taiwanese Journal of Mathematics
出版狀態已出版 - 10月 2011


深入研究「A note on circular colorings of edge-weighted digraphs」主題。共同形成了獨特的指紋。