²é¿´: 561  |  »Ø¸´: 3

hzsh2009

Í­³æ (СÓÐÃûÆø)

[ÇóÖú] graph coloring

Suppose a map is made by drawing n intersecting circles. Show that the regions in this map can be properly 2-colored


Solve by assigning colors based on number of circles that contain a region
»Ø¸´´ËÂ¥
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

YANGZL

½ð³æ (СÓÐÃûÆø)

¡¾´ð°¸¡¿Ó¦Öú»ØÌû

¡ï
soliton923(½ð±Ò+1): лл²ÎÓëÌÖÂÛ~~Äã»ØÌû¾ÍÐÐÁË£¬Ã»ÓбØÒªÃ¿¸ö¶¼ÐèÒª¾Ù±¨¸ø°æÖ÷´¦Àí£¬ºÇºÇ 2011-10-01 17:56:42
Ó¦¸Ã²»¿ÉÒÔ¡£
ԲȦÏཻºó£¬¾ÍÊÇÆ½ÃæÍ¼¡£ÓÃËÄÉ«¾Í¿ÉÒÔ¡£

¹Ø¼üÊÇÔõôÏཻµÄ£¿Èç¹ûÏཻ³ö Kuratowski graph k3,3 k5£¬ÄÇô4ɫҲ²»¹»¡£
տɵ£¨ÇóÕæ£©
2Â¥2011-10-01 12:57:53
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

hzsh2009

Í­³æ (СÓÐÃûÆø)

ÒýÓûØÌû:
2Â¥: Originally posted by YANGZL at 2011-10-01 12:57:53:
Ó¦¸Ã²»¿ÉÒÔ¡£
ԲȦÏཻºó£¬¾ÍÊÇÆ½ÃæÍ¼¡£ÓÃËÄÉ«¾Í¿ÉÒÔ¡£

¹Ø¼üÊÇÔõôÏཻµÄ£¿Èç¹ûÏཻ³ö Kuratowski graph k3,3 k5£¬ÄÇô4ɫҲ²»¹»¡£

Ê×ÏÈËüÊÇÒ»¸öplanar graph£¨ÌâÄ¿¸øµÄ£©£¬È»ºóËüÓ¦¸Ã¾ÍÊÇԲȦÏཻ£¬Èç¹ûÖ»Óж¥µã½»²»ËãÏàÁ¬µÄ¡£ËùÒÔ2É«¹»ÁË¡£µ«²»ÖªµÀÔõô֤¡£¡£
3Â¥2011-10-01 20:50:30
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

YANGZL

½ð³æ (СÓÐÃûÆø)

¡¾´ð°¸¡¿Ó¦Öú»ØÌû

²»»á¡£
ÏÂÃæµÄÏë·¨£¬½ö¹©²Î¿¼¡£
Cycle graphs shi 2×ÅÉ«µÄ¡£2¸ö circles intersect£¬»á»áÐγÉ3¸öcircles¡£n intersecting circles£¬»á³É²»³¬¹ý¡°×éºÏÊý¡±µÄcircles¡£
²»ÖªµÀÕâ¸ö˼·ÓÐûÓÐÓá£

°³²»ÊÇѧÊýѧµÄ£¬Ö»ÊÇÊýѧ°®ºÃÕß¡£Ã»ÓÐÄÜÁ¦±£Ö¤½â´ðµÄ¼ÛÖµ¡£

°³Ï¹Ï룺
made by drawing£¬¿É²»Äܱ£Ö¤½á¹ûÒ»¶¨Æ½ÃæÍ¼°¡£¡
k3,3 k5 Ò²ÊÇÔÚÆ½ÃæÉÏdrawnµÄ°¡£¬Ö»ÊÇËüÃǵÄÁ¬½Ó·½Ê½ÆæÌØÁ˵㡣
տɵ£¨ÇóÕæ£©
4Â¥2011-10-02 09:05:55
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
Ïà¹Ø°æ¿éÌø×ª ÎÒÒª¶©ÔÄÂ¥Ö÷ hzsh2009 µÄÖ÷Ìâ¸üÐÂ
×î¾ßÈËÆøÈÈÌûÍÆ¼ö [²é¿´È«²¿] ×÷Õß »Ø/¿´ ×îºó·¢±í
[»ù½ðÉêÇë] Ϊʲô×ÊÖúÊý¸÷´ó¸ßУ¶¼´´Ð¸ߣ¬×Ô¼ºÉêÇëÔõô¾ÍÕâôÄÑ +9 Kittylucky 2026-08-27 9/450 2026-08-28 01:08 by jurkat.1640
[»ù½ðÉêÇë] ÄÄλ¸ßÈËÖÐÁË£¬°Ñ²éѯµ½µÄ½ØÍ¼Ìù³öÀ´ÈÃÎÒ¿´¿´£¬ÈÃÎÒ³¤³¤¼ûʶ +5 yuleib84 2026-08-26 6/300 2026-08-28 00:02 by yudaoqian88
[»ù½ðÉêÇë] »ù½ðδÖУ¬ÕâÖÖ´ð¸´ÊÇÄ£°åÂ𣿠+5 zhaosm1982 2026-08-27 6/300 2026-08-27 16:00 by lfy8008
[»ù½ðÉêÇë] ¿´°åÉÏÕâô¶àÖеģ¬ÓеãÏñ50ÈËȺÀï49¸öÈ˶¼ÊÇÆ­×ÓµÄÄÇÖָоõ¡­¡­ +5 a089 2026-08-26 6/300 2026-08-27 14:05 by jonewore
[»ù½ðÉêÇë] Ôõô¿´Çà»ùÖÐÁËûÓа¡ +5 Ò¶¾Å΢ 2026-08-26 5/250 2026-08-27 10:35 by l_zh2008
[½Ìʦ֮¼Ò] ÊÛSCIÒ»ÇøÎÄÕ£¬ÎÒ:8.O.551.O.5.4,¿ÆÄ¿È«,¿ÉÙ¤¼± +3 LIbGuocjEEYw 2026-08-26 4/200 2026-08-27 04:33 by Ie9AyIAvGbvs
[˶²©¼ÒÔ°] ÊÛSCIÒ»ÇøT0PÎÄÕ£¬ÎÒ:8.O.55.1.O.54,¿ÆÄ¿ÆëÈ«,¿É+¼± +3 LIbGuocjEEYw 2026-08-26 4/200 2026-08-27 02:01 by Ie9AyIAvGbvs
[»ù½ðÉêÇë] 2026ÄêµÄ¹ú¼ÒÉç¿Æ»ù½ðÏîĿͨѶÆÀÉóµÄйæÔòÓëж¯Ïò¡¢ÐÂÌôÕ½ +7 process2012 2026-08-23 10/500 2026-08-26 19:23 by hmhminy
[»ù½ðÉêÇë] Ôõô²é°¡ +5 huang1991js 2026-08-26 5/250 2026-08-26 16:09 by Equinoxhua
[»ù½ðÉêÇë] ·¶½øÖоÙÒ»ÎĵÄÖÐÐÄ˼Ïë +9 Ñ׻ƹóëÐ 2026-08-22 10/500 2026-08-26 15:40 by semaglutide
[»ù½ðÉêÇë] ÄÜ·ñÍ˳ö²ÎÓëµÄÃæÉÏÏîÄ¿½â³ýÏÞÏî +23 koalala 2026-08-24 26/1300 2026-08-26 14:29 by ±¦±´³æ×Ó
[»ù½ðÉêÇë] Ϊʲô¹ú×ÔÈ»²»ÄÜÖ±½Ó¹«²¼ +4 bjdxyxy 2026-08-26 4/200 2026-08-26 13:12 by qingmu1201
[»ù½ðÉêÇë] ¹úºÏÀïÃæÄÜ¿´µ½ÁË +7 Ò»»³Ü°Çï 2026-08-26 7/350 2026-08-26 11:23 by zhaosm1982
[»ù½ðÉêÇë] ϵͳ½ø²»È¥ +4 yanglien 2026-08-26 5/250 2026-08-26 11:10 by wenfengw83
[Ö°³¡ÈËÉú] ѧÉúײ¼û¸¨µ¼Ô±ËÍÍâÂô£¬µÚ¶þÌìÈ«°à¶¼³ÁĬÁË +3 ¾¨ÓãÈÚ½ð_Õã½­_É 2026-08-22 3/150 2026-08-26 09:01 by zzuzxg
[»ù½ðÉêÇë] Èç¹û´Ë¿ÌÄãÕýÔÚΪ¹ú»ù¸Ðµ½½¹ÂÇ£¬²»·ÁÀ´ÌýÌýÕâÊס¶»ù½ðÖ®Íâ¡· +8 scalable 2026-08-24 8/400 2026-08-25 12:52 by jnhyjjm
[»ù½ðÉêÇë] ûÓÐÈκÎÏûÏ¢-ÊDz»ÊǾÍÁ¹ÁË +9 ͼÀ²Í¼À² 2026-08-24 10/500 2026-08-25 11:59 by ÄϺ£Ð¡¸ç
[»ù½ðÉêÇë] ÈËÆø²»ÐÐÁË +11 fansofjerry 2026-08-21 11/550 2026-08-25 11:04 by ¹Â¶ÀµÄÓ¢ÐÛ6
[½Ìʦ֮¼Ò] Ìø²ÛºóÔÚÑÐÏîÄ¿Ôõô°ì£¿ +5 ¼òµ¥»¯xn 2026-08-22 10/500 2026-08-23 12:38 by ¼òµ¥»¯xn
[»ù½ðÉêÇë] Ó¦¸ÃÊÇÏÂÖÜÈý26ÈÕ¹«²¼Á˰ɣ¿ +4 ¹þ¹þ¸ò£¿ 2026-08-21 4/200 2026-08-21 10:58 by Vivilian
ÐÅÏ¢Ìáʾ
ÇëÌî´¦ÀíÒâ¼û