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1 vote
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coloring of an interval graph with constraints

Given an interval graph that represents a set of tasks, in a given period of time, to be assigned to a set of employees, the objective is to find a minimum coloring of this graph such that the total ...
Farah Mind's user avatar
2 votes
1 answer
177 views

Like transitive reduction, but removing vertices rather than edges?

Suppose I have a directed graph $G = (V, E)$ (or, which is the same, a relation on the set $V$ as defined by the adjacency matrix) that may contain three vertices $x, y, z$, such that $xy, xz, yz \in ...
Ignat Insarov's user avatar
0 votes
2 answers
1k views

Can someone point out why these directed graphs aren't equivalence relations?

As far as I can tell, these two directed graphs are reflexive, symmetric and transitive.
Luke D's user avatar
  • 11
2 votes
1 answer
69 views

Algorithm for getting symetric vertex sets of undirected graph

For my application problem, I am searching for an algorithm that can find all symmetric vertex sets of an undirected labeled graph. My definition of symmetric vertex set is: Let $G$ be a graph with ...
Pepper M's user avatar
  • 325
2 votes
1 answer
936 views

Simplest way to check edge set for transitivity

I'm playing around with tournaments and currently have the problem that I need to check whether a given subset of the edges of a tournament is transitive (it need not be acyclic). I'm aware that I can ...
G. Bach's user avatar
  • 2,019