Title of article :
Planar Turán Numbers on Short Cycles of Consecutive Lengths
Author/Authors :
Du ، Liangli Department of Mathematics - School of Mathematics and Finance - Chuzhou University , Wang ، Bing Department of Mathematics - School of Mathematics and Finance - Chuzhou University , Zhai ، Mingqing Department of Mathematics - School of Mathematics and Finance - Chuzhou University
Abstract :
LetHbe a family of graphs. The planar Turán number ofH, denoted by exP(n,H), is the maximum number of edges over all planar graphs on n vertices that do not contain any H ∈ H as a subgraph. In this paper, we obtain sharp bounds of exP(n, {C3,C4}) and exP(n, {C4,C5}), respectively. We also give infinitely many graphs which attain these bounds.
Keywords :
Turán number , Planar graph , Consecutive cycles
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
