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Omni-MATH / The following operation is allowed on a finite graph: Choose an arbitrary cycle…

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problem

The following operation is allowed on a finite graph: Choose an arbitrary cycle of length 4 (if there is any), choose an arbitrary edge in that cycle, and delete it from the graph. For a fixed integer n≥4{n\ge 4}, find the least number of edges of a graph that can be obtained by repeated applications of this operation from the complete graph on nn vertices (where each pair of vertices are joined by an edge). [i]
Plain-text mathematical notation (without MathML)
The following operation is allowed on a finite graph: Choose an arbitrary cycle of length 4 (if there is any), choose an arbitrary edge in that cycle, and delete it from the graph. For a fixed integer n≥4, find the least number of edges of a graph that can be obtained by repeated applications of this operation from the complete graph on n vertices (where each pair of vertices are joined by an edge).

[i]
Original LaTeX notation
The following operation is allowed on a finite graph: Choose an arbitrary cycle of length 4 (if there is any), choose an arbitrary edge in that cycle, and delete it from the graph. For a fixed integer ${n\ge 4}$, find the least number of edges of a graph that can be obtained by repeated applications of this operation from the complete graph on $n$ vertices (where each pair of vertices are joined by an edge).

[i]

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Source and history

task_id
9516dd9d-3cdc-5f01-b106-2aceb27b4713
task_key
test--9516dd9d-3cdc-5f01-b106-2aceb27b4713
task_revision_id
1
config / split
/ test

Official source

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