Giants’ Cueto wins NL League Player of the Week, plus notes and lineup

Giants’ Cueto wins NL League Player of the Week, plus notes and lineup ATLANTA — A starting pitcher must have two good games to get Player of the Week. Cueto won the National League honors for last week, when he pitched a two-hit shutout at home and held the Rockies to one earned run in six innings at Coors Field. [...] the Giants have won all seven of Cueto’s last starts. Minnesota’s Joe Mauer won in the American League. Over the past three seasons the Giants have been a May juggernaut, going 61-26 heading into Tuesday night’s final game of the month. The Giants have some cause to hope that this June will be better, despite a schedule that looks tougher than May’s in terms of teams they have to play and where. If this trio can maintain a semblance of its May self, the Giants should be able to avoid another losing June as long as they can hit some. Dick Tidrow, the Giants’ executive pitching guru, must have worn a mile-wide smile after seeing the reports from the minors Monday. The four Giants starters at Triple-A, Double-A, High-A and Low-A — Clayton Blackburn, Adelberto Mejia, Sam Coonrod and Phil Bickford — pitched a combined 27 1/3 innings and allowed two earned runs, a 0.66 ERA. Blackburn, allowing one earned run in his past 14 innings over two starts and a short relief appearance. Giants folks raved about Coonrod’s power arm in spring training. Tuesday’s lineup against left-hander Matt Wisler, another really good young pitcher on Atlanta’s staff. Henry Schulman is a San Francisco Chronicle staff writer.