k-partite graph

A $k$ -partite graph is a graph with a chromatic number of $k$ .

An alternate definition of a $k$ -partite graph is a graph where the vertices are partitioned into $k$ subsets with the following conditions:

1.
No two vertices in the same subset are adjacent.
2.
There is no partition of the vertices with fewer than $k$ subsets where condition 1 holds.

These two definitions are equivalent. Informally, we see that a colour can be assigned to all the vertices in each subset, since they are not adjacent to one another. Furthermore, this is also an optimal colouring, since the second condition holds.

An example of a 4-partite graph:

单词	KpartiteGraph
释义	k-partite graph A $k$ -partite graph is a graph with a chromatic number of $k$ . An alternate definition of a $k$ -partite graph is a graph where the vertices are partitioned into $k$ subsets with the following conditions: 1. No two vertices in the same subset are adjacent. 2. There is no partition of the vertices with fewer than $k$ subsets where condition 1 holds. These two definitions are equivalent. Informally, we see that a colour can be assigned to all the vertices in each subset, since they are not adjacent to one another. Furthermore, this is also an optimal colouring, since the second condition holds. An example of a 4-partite graph:
随便看	trimmed mean TrimorphicNumber trimorphic number TripleCrossProduct triple cross product TripleScalarProduct triple scalar product TrisectionOfAngle trisection of angle Triskaidekaphobia triskaidekaphobia TrivialValuation trivial valuation TrulyRandomNumbers truly random numbers TruncatedCone truncated cone Truncations Truncations TruthFunction truth function TruthTable truth table TruthvalueSemanticsForClassicalPropositionalLogic truth-value semantics for classical propositional logic