AbstractGiven a multigraph G, a sequence (h1,…, hm) of nonnegative integers h1≥… ≥ hmis color‐feasible for G if there is an edge‐coloring H1,…, Hmwhere Hihas exactly hiedges (i=1,…, m). It is known that the set C(G) of color‐feasible sequences of G is partially ordered. We show that if G is simple with maximum degree d, then all maximal sequences of C(G) have at most d+1 nonzero entries. This result can be extended to multigraphs. Furthermore, if the odd elementary cycles of a multigraph G satisfy some specified conditions then all maximal sequences have at most d+