An extremal graph problem on a grid and an isoperimetric problem for polyominoes

DOI10.37236/12133MaRDI QIDQ6126448

Andrew Vince

Publication date: 9 April 2024

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Enumeration in graph theory (05C30) Planar graphs; geometric and topological aspects of graph theory (05C10) Isoperimetric problems for polytopes (52B60) Polyominoes (05B50)

Cites Work

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• Vertex isoperimetric inequalities for a family of graphs on \(\mathbb{Z}^k\)
• Reconstructing convex polyominoes from horizontal and vertical projections
• Extremal topological and geometric problems for polyominoes
• Edge-isoperimetric inequalities in the grid
• Algebraic languages and polyominoes enumeration
• Ideals generated by 2-minors, collections of cells and stack polyominoes
• Edge isoperimetric theorems for integer point arrays
• Extremal \(\{ p, q\}\)-animals
• Discrete Isoperimetric Problems
• Isoperimetry in integer lattices
• A Prime Example of the Strong Law of Small Numbers
• Optimal numberings and isoperimetric problems on graphs
• Sets of Lattice Points which Contain a Maximal Number of Edges

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