Maximum star densities

DOI10.1556/012.2018.55.2.1395zbMATH Open1399.05130arXiv1708.01822OpenAlexW2745167165MaRDI QIDQ3176667

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Publication date: 23 July 2018

Published in: Studia Scientiarum Mathematicarum Hungarica (Search for Journal in Brave)

Abstract: Given an integer $kgeq2$ and a real number $gammain[0,1]$, which graphs of edge density $gamma$ contain the largest number of $k$-edge stars? For $k=2$ Ahlswede and Katona proved that asymptotically there cannot be more such stars than in a clique or in the complement of a clique (depending on the value of $gamma$). Here we extend their result to all integers $kge2$.

Full work available at URL: https://arxiv.org/abs/1708.01822

zbMATH Keywords

starsgraphonshomomorphism densities

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Enumeration in graph theory (05C30)

Related Items (9)

Minimum dilation stars ⋮ On the maximum number of copies of H in graphs with given size and order ⋮ On a problem of Ahlswede and Katona ⋮ Ordered and colored subgraph density problems ⋮ Threshold graphs maximise homomorphism densities ⋮ MAXIMUM MASS OF A CLASS OF COLD COMPACT STARS ⋮ Unified approach to the generalized Turán problem and supersaturation ⋮ On a Conjecture of Nagy on Extremal Densities ⋮ The feasible region of induced graphs

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