½üÈÕ£¬Êýѧϵ¿Â·öÓ¢½ÌÊںͲ©Ê¿ÉúÍõ溡¢Ñ¦ÒæÈüÔÚͼÆ×Tur¨¢nÐͼ«ÖµÎÊÌâ·½Ãæ»ñµÃ³ÁÒª½øÕ¹£¬ÓйØ×êÑгɾÍÒÔ¡°On a conjecture of spectral extremal problems¡±ÎªÌâ°ä·¢ÔÚ×éºÏͼÂÛÁìÓòµÄ¶¥¼¶ÆÚ¿¯¡¶Journal of Combinatorial Theory£¬Series B¡·ÉÏ¡£¸ÃÂÛÎĿ·öÓ¢½ÌÊÚΪͨѶ×÷Õߣ¬²©Ê¿ÉúÍõæºÎªµÚÒ»×÷Õߣ¬Ð±¦GGΪµÚÒ»ÊðÃûµ¥Ôª¡£

Æ×¼«ÖµÎÊÌâÊÇ×éºÏͼÂÛÁìÓòÖÐÒ»¸ö³ÁÒªºÍ»îÔ¾µÄ×êÑз½Ïò£¬¸ÃÎÊÌâ×êÑиø¶¨Í¼ÀàÖÐijЩÆ×²ÎÁ¿µÄ¼«Öµ¡£Í¼µÄÆ×Tur¨¢nÐͼ«ÖµÎÊÌâÊÇÒ»ÀྵäµÄÆ×¼«ÖµÎÊÌ⣬ҲÊÇͼµÄTur¨¢nÐͼ«ÖµÎÊÌâÔÚͼÆ×ÀíÂÛÖеÄÑÓ³¤¡£½üÄêÀ´£¬´ËÀàÎÊÌâÊܵ½À´×ÔÊÀ½ç¸÷µØ¶à¶à³ÛÃûѧÕߵĹØ×¢£¬²¢»ñµÃÁËһϵÁгÁÒªÍ»ÆÆ¡£ Cioab?, DesaiºÍTait [The spectral radius of graphs with no odd wheels. European J. Combin., 99: 103420, 2022] Ìá³öÁËÈçϲ²⣺¸ø¶¨Í¼F, ÈôÊÇFµÄ¼«ÖµÍ¼Äܹ»Í¨¹ýTur¨¢nͼ¼ÓÉϳ£ÊýÌõ±ßµÃµ½£¬Ôòµ±n×ã¹»´óʱ£¬²»Ô̺¬F×÷Ϊ×ÓͼµÄn½×ͼÖÐÁÚ½ÓÆ×°ë¾¶´ïµ½×î´óµÄͼ¿Ï¶¨Ò²ÊǽûÓÃFµÄͼÖбßÊý´ïµ½×î´óµÄͼ¡£±¾ÎÄÀûÓÃÆ×²»±äÐÔ¶¨ÀíºÍ½á¹¹·ÖÎöµÄ²½Ö裬³¹µ×½â¾öÁËÉÏÊö²Â²â£¬²¢¸ø³öÁËÒ»¸ö±ÈCioab?, DesaiºÍTaitµÄ²Â²â¸üÇ¿µÄÁ˾֡£¸ÃÎÄÖ¤ÁËÈ»£º¸ø¶¨Í¼F, ÈôÊÇFµÄ¼«ÖµÊýΪTur¨¢nͼµÄ±ßÊý¼ÓÉÏÒ»¸ö³£Êýʱ£¬Ôòµ±n×ã¹»´óʱ£¬²»Ô̺¬F×÷Ϊ×ÓͼµÄn½×ͼÖÐÁÚ½ÓÆ×°ë¾¶´ïµ½×î´óµÄͼ¿Ï¶¨Ò²ÊǽûÓÃFµÄͼÖбßÊý´ïµ½×î´óµÄͼ¡£ÕâÏî×êÑй¤×÷¼«´óµØÍƶ¯ÁËÆ×¼«ÖµÎÊÌâµÄ×êÑС£
½üÄêÀ´¿Â·öÓ¢ÍŶÓÔÚͼºÍ³¬Í¼µÄ¼«ÖµÎÊÌâµÄ×êÑÐÉÏ×ö³öÁ˺öഴÐÂÐÔµÄ×êÑгɾ͡£ÔÚJournal of Combinatorial Theory, Series B¡¢SIAM Discrete Mathematics ¡¢ Journal of Graph Theory¡¢European Journal of CombinatoricsµÈѧÊõÆÚ¿¯Éϰ䷢ѧÊõÂÛÎÄ160ÓàÆª£¬Ö÷³Ö¶àÏî¹ú¶ÈÌìÈ»¿ÆÑ§»ù½ðÏîÄ¿¡£±ÏÒµµÄ¶àλ²©Ê¿»ñµÃ¹ú¶ÈÌìÈ»¿ÆÑ§»ù½ðÇàÄêÏîÄ¿ºÍÃæÉÏÏîÖ÷ÕÅÔÞÖú¡£¿Â·öÓ¢½ÌÊÚ½ñÄê¸ú°²»Õ´óѧ¡¢ºþÄÏʦ·¶´óѧºÏ×÷³É¹¦ÉêÇëµ½¹ú¶ÈÌìÈ»¿ÆÑ§»ù½ð³ÁµãÏîÄ¿¡£
ÂÛÎÄÁ´½Ó£ºhttps://doi.org/10.1016/j.jctb.2022.11.002