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Omni-MATH / Let r be a positive integer. Show that if a graph G has no cycles of length at most 2r, then it has at most |V|²⁰¹⁶ cycles of length exactly 2016r, where |V| denotes the number of …

Problem

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problem

Let rr be a positive integer. Show that if a graph GG has no cycles of length at most 2r2 r, then it has at most |V|2016|V|^{2016} cycles of length exactly 2016r2016 r, where |V||V| denotes the number of vertices in the graph G.
Plain-text mathematical notation (without MathML)
Let r be a positive integer. Show that if a graph G has no cycles of length at most 2r, then it has at most |V|²⁰¹⁶ cycles of length exactly 2016r, where |V| denotes the number of vertices in the graph G.
Original LaTeX notation
Let $r$ be a positive integer. Show that if a graph $G$ has no cycles of length at most $2 r$, then it has at most $|V|^{2016}$ cycles of length exactly $2016 r$, where $|V|$ denotes the number of vertices in the graph G.

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Source and history

task_id
2c16c23e-d821-501b-89f3-383df495679c
task_key
test--2c16c23e-d821-501b-89f3-383df495679c
task_revision_id
1
config / split
/ test

Official source

initial import