Anti-Ramsey numbers in complete split graphs

A subgraph of an edge-colored graph is rainbow if all of its edges have different colors. The anti-Ramsey number  ar(G,H)ar(G,H) is the maximum number of colors in an edge-coloring of GG with no rainbow copy of HH. Anti-Ramsey numbers were introduced by Erdős et al. (1973) and studied in numerous papers. Originally a complete graph was considered as GG, but afterwards also other graphs were used as host graphs.We consider a complete split graph as the host graph and discuss some results for the graph HH containing short cycles or triangles with pendant edges. Among others we show that ar(Kn+Ks¯,C3+)=ar(Kn+Ks¯,C3)=n+s−1 for n,s≥1n,s≥1, where C3+ denotes a triangle with a pendant edge.