Abstract
AbstractThe Turán number is the maximum number of edges in an ‐free graph on vertices. Let be any tree. The odd‐ballooning of , denoted by , is a graph obtained by replacing each edge of with an odd cycle containing the edge, and all new vertices of the odd cycles are distinct. In this paper, we determine the exact value of for sufficiently large and being good, which generalizes all the known results on for being a star, due to Erdős, Füredi, Gould, and Gunderson (1995), Hou, Qiu, and Liu (2018), and Yuan (2018), and provides some counterexamples with chromatic number three to a conjecture of Keevash and Sudakov (2004), on the maximum number of edges not in any monochromatic copy of in a 2‐edge‐coloring of a complete graph of order .
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
