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Yoshikawa [Yo] conjectured that a certain set of moves on marked graphdiagrams generates the isotopy relation for surface links in ${\mathbb R}^4$,and this was proved by Swenton [S] and Kearton and Kurlin [KK]. In this paper,we find another proof of this fact for the case of 2-links (surface links withspherical components). The proof involves a version of Roseman's theorem [R]for branch-free broken surface diagrams of 2-links and a construction of markedgraphs from branch-free broken surface diagrams.

Yoshikawa moves on marked graphs via Roseman's theorem