Here is the weekly manga sales ranking for May 31st - June 6th.

*1, 1,580,757 1,580,757 One Piece vol.58 Note: release date was June 4th.
*2, *,465,713 *,465,713 Bleach vol.45
*3, *,241,360 *,241,360 D.Gray-man vol.20
*4, *,112,709 *,414,702 Vagabond vol.33
*5, *,109,255 *,646,359 Saint Young Men vol.5
*6, *,*98,970 *,*98,970 Kaichou wa Maid-sama! vol.10
*7, *,*86,147 *,*86,147 Tegami Bachi vol.10
*8, *,*77,674 *,*77,674 Kuroko no Basket vol.7
*9, *,*73,546 *,*73,546 Beelzebub vol.6
10, *,*52,220 *,*52,220 Tobaku Mokushiroku Kaiji: Kazuya-hen vol.3

11, *,*46,374 *,*46,374 Kiss x Sis vol.6
12, *,*45,926 *,*45,926 Kochira Katsushika-ku Kamearikouen-mae Hashutsujo vol.170
13, *,*45,575 *,*45,575 Rosario+Vampire Season II vol.7
14, *,*44,899 *,*44,899 Sengoku Tenshouki vol.9
15, *,*39,059 *,471,646 Detective Conan vol.68
16, *,*36,485 *,*36,485 Sengoku Gaiden vol.3
17, *,*33,608 *,113,870 Switch Girl!! vol.12
18, *,*33,214 *,400,012 Fairy Tail vol.21
19, *,*30,019 *,175,570 Hetalia Axis Powers vol.3 Special Edition
20, *,*29,188 *,*60,586 I am a Hero vol.3

21, *,*27,137 *,104,917 Koibana! Koiseyo Hanabi vol.8
22, *,*26,994 *,*58,130 Moon vol.6
23, *,*26,466 *,*26,466 Prince of After School vol.1
24, *,*25,402 *,*25,402 Higanjima vol.31
25, *,*23,644 *,189,464 Major vol.76
26, *,*23,469 *,*23,469 Kiss x Sis vol.6 with OVA
27, *,*22,882 *,256,709 Kekkaishi vol.29
28, *,*22,551 *,*22,551 Mayoi Neko Overrun! Character Navi Book Nekokan!
29, *,*22,377 *,157,468 Moteki vol.4
30, *,*22,323 *,*48,744 Pocket Monster Special vol.35

Source: Oricon Manga Ranking

Weekly Light Novel Ranking for May 31 - Jun 6
*1, 15,312 *23,199 Migawari Hakushaku no Hanayome Kagyo vol.1
*2, 12,600 *20,253 Mismarka Kokokuki vol.7
*3, *7,264 256,340 Durarara!! vol.1
*4, *6,471 202,952 Durarara!! vol.2
*5, *6,187 **6,187 Koi no Dress to Tsuki no Furu Shiro
*6, *6,162 185,760 Yojouhan Shinwa Taikei
*7, *6,147 *12,347 Monster Hunter Senko no Kariudo vol.2
*8, *6,013 177,572 Durarara!! vol.3
*9, *5,973 158,920 Durarara!! vol.4

Source: Oricon Novel Ranking