Question
Download Solution PDFThe K-coloring of an undirected graph G = (V, E) is a function C: V ➝ {0, 1, ......, K-1} such that c(u) ≠ c(v) for every edge (u, v) ∈ E Which of the following is not correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFA k- coloring of a graph G is mapping f: V(G) -> {set of k elements called colors}, such that adjacent vertices are mapped onto different elements.
A graph is called k – colourable, if it has a k-coloring. A k-coloring of a graph G(V, E) is a partitioning V = V1 U V2 U V3 ………… U Vk into at most k independent sets of G.
Properties of K- colourable graph are:
1) A cycle of length n>=3 is – chromatic if n is even and 3- chromatic if n is odd
2) A graph is bi- colourable (2- chromatic) if and only if it has no odd cycles.
3) A non - empty graph G is bi colourable if and only if G is bipartite.Last updated on Jul 7, 2025
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