2022/01/03 by Chen, Ming-Zhu, Wang, Ning, Yuan, Long-Tu +1 · 1 citation
#05C35 #05C50 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2201.00453
The bipartite Tur'an number of a graph H, denoted by ex(m,n; H), is the maximum number of edges in any bipartite graph G=(X,Y; E) with |X|=m and |Y|=n which does not contain H as a subgraph. In this paper, we determined ex(m,n; Fℓ) for arbitrary ℓ and appropriately large n with comparing to m and ℓ, where F_ℓ is a linear forest which consists of ℓ vertex disjoint paths. Moreover, the extremal graphs have been characterized. Furthermore, these results are used to obtain the maximum spectral radius of bipartite graphs which does not contain Fℓ as a subgraph and characterize all extremal graphs which attain the maximum spectral radius.