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Results tagged with graph-theory
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user 5963
Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.
1
vote
Create matrix containing values in [0,1] where sum of all diagonals and anti-diagonals is fixed
The given constraints are a system of linear inequalities, so you can find a feasible solution (or prove that none exists) by feeding these constraints to a linear program (LP) solver with some arbitr …
- 8,501
12
votes
Accepted
Existence of a sink in directed graphs with a certain structure
Your conjectures are proven in the paper "Congestion Games with Player-Specific Payoff Functions" by I. Milchtaich, published in Games and Economic Behavior in 1996.
Usually, the term "congestion gam …
- 8,501
11
votes
Accepted
Non-negative quadratic maximization
First, note that the condition that $A$ be positive semidefinite (PSD) doesn't buy you anything. Replacing $A$ by $A+kI$ changes the objective value of any feasible solution by $k$, so if we could so …
- 8,501
3
votes
Accepted
Random Walks in $Z^2$/$Z^2$-intrinsic characterization of Euclidean distance
As written the statement is false for $n=3$: note that $p_3(2,2) = 0$ but $p_3(3,0) > 0$, while $|(2,2)| < |(3,0)|$. Similar counterexamples exist for all $n\geq 5$. So for larger $n$ you would at l …
- 8,501