论文信息 - Generalized outerplanar Tur\'an number of short paths

Generalized outerplanar Tur\'an number of short paths

Let H be a graph. The generalized outerplanar Turán number of H, denoted by fOP(n,H), is the maximum number of copies of H in an n-vertex outerplanar graph. Let Pk be the path on k vertices. In this paper we give an exact value of fOP(n, P4) and a best asymptotic value of fOP(n, P5). Moreover, we characterize all outerplanar graphs containing fOP(n, P4) copies of P4.

Ervin GyHori | Addisu Paulos | Chuanqi Xiao

[1] Noga Alon,et al. Many T copies in H-free graphs , 2014, Electron. Notes Discret. Math..

[2] Ryan R. Martin,et al. The maximum number of paths of length four in a planar graph , 2020, Discret. Math..

[3] Noga Alon,et al. On The Number of Subgraphs of Prescribed Type of Planar Graphs With A Given Number of Vertices , 1984 .

[4] L. Moser,et al. AN EXTREMAL PROBLEM IN GRAPH THEORY , 2001 .

[5] S. Hakimi,et al. On the number of cycles of length k in a maximal planar graph , 1979, J. Graph Theory.

[6] Ryan R. Martin,et al. Counting paths, cycles and blow-ups in planar graphs , 2021 .

[7] P. Erdos,et al. A LIMIT THEOREM IN GRAPH THEORY , 1966 .

[8] Ervin Györi. On the number of C5's in a triangle-free graph , 1989, Comb..

[9] P. Erdös. On the structure of linear graphs , 1946 .

[10] J. Sheehan,et al. On the number of complete subgraphs contained in certain graphs , 1981, J. Comb. Theory, Ser. B.

[11] Generalised outerplanar Turán numbers and maximum number of k-vertex subtrees , 2021, Discrete Applied Mathematics.