The circular chromatic number of series-parallel graphs of large odd girth Original Research Article

Suppose G is a series-parallel graph. We prove that if G has odd girth at least 6k−1 then χc(G)⩽8k/(4k−1); if G has odd girth at least 6k+1 then χc(G)⩽(4k+1)/2k; if G has odd girth at least 6k+3 then χc(G)⩽(4k+3)/(2k+1).