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Omni-MATH / For a finite graph G, let f(G) be the number of triangles and g(G) the number of tetrahedra formed by edges of G. Find the least constant c such that g(G)³≤c⋅f(G)⁴ for every graph …

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problem

For a finite graph GG, let f(G)f(G) be the number of triangles and g(G)g(G) the number of tetrahedra formed by edges of GG. Find the least constant cc such that g(G)3≤c⋅f(G)4g(G)^3\le c\cdot f(G)^4 for every graph GG. [i]
Plain-text mathematical notation (without MathML)
For a finite graph G, let f(G) be the number of triangles and g(G) the number of tetrahedra formed by edges of G. Find the least constant c such that g(G)³≤c⋅f(G)⁴ for every graph G.

[i]
Original LaTeX notation
For a finite graph $G$, let $f(G)$ be the number of triangles and $g(G)$ the number of tetrahedra formed by edges of $G$. Find the least constant $c$ such that \[g(G)^3\le c\cdot f(G)^4\] for every graph $G$.

[i]

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Source and history

task_id
29e68a92-b3b7-5b19-86b4-b06de1798d6d
task_key
test--29e68a92-b3b7-5b19-86b4-b06de1798d6d
task_revision_id
1
config / split
/ test

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