Questions on graph coloring, an assignment of colors to elements of a graph subject to specific constraints.

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2
votes
2answers
135 views

Application of Four color theorem

I was reading up on Four color theorem and am wondering if there is any practical application of it .( I dont think seperating the map into four different colors can be considered an application) I ...
0
votes
1answer
124 views

Find largest chromatic number of a full binary tree [closed]

This is a Discrete Math/Combinatorics Question from my hw…but I don't really understand the question. Find largest chromatic number of a full binary tree given the following depths: (Check all ...
3
votes
3answers
228 views

Characterisation of graphs that are not 3-colorable

We know that all graphs with odd cycles (odd number of vertices) are not 2-colorable. Is there a similar characterisation for 3-colorability? I am looking for undirected graphs that are not ...
4
votes
1answer
144 views

A variation of the graph coloring problem

Given a set of colors $M$ and a graph $G=(V,E)$. Allocate the colors to minimize the number edges with same color on the two vertices of the edge (i.e. minimize pairs of adjoining vertices with same ...
1
vote
2answers
125 views

Calculate number of ways to color matrix using inclusion-exclusion principle

This was asked in a recent contest. The question asked to count the number of ways to color an $M \times N$ matrix with $K$ colours such that no two adjacent cells (sharing an edge) have the same ...
2
votes
1answer
98 views

Strategic vertex labeling

We are given a graph $G=(V,E)$ with positive edge weights $w_{i}$ and numerical {0,1,-1} labels $l$ for all vertices . We know that $G$ has a subset $G'$ with all vertices labeled 0. The problem is to ...
1
vote
1answer
56 views

Prove that 2-Colourability is in L from Undir-Reachability is in L

Let Undir-Reachability be the following problem: given an undirected graph G and two specified vertices s and t in G, is there a path from s to t in G? I need to prove that the 2-Colourability is in ...
5
votes
1answer
155 views

6-coloring of a tree in a distributed manner

I have some difficulties in understanding distributed algorithm for tree 6 - coloring in $O(\log^*n)$ time. The full description can be found in following paper: Parallel Symmetry-Breaking in Sparse ...
2
votes
1answer
188 views

Distributed 6-color Vertex Coloring

I am trying to understand the distributed 6-color algorithm for vertex coloring (on page 10). Here is a short description Idea of the algorithm: We start with color labels that have $\log n$ bits. ...
10
votes
2answers
504 views

Chromatic polynomial of a square

Consider a square, ABCD. Intuitively it seemed to me that its chromatic polynomial is $\lambda(\lambda - 1)(\lambda - 1)(\lambda - 2)$ where there are $\lambda$ colours available.. That is there are ...
5
votes
0answers
104 views

Beating fair colorings with few edges

I have been investigating parallel algorithms to compute certain two-dimensional dynamic programming recursions (on natural parameters); see also here. Under certain assumptions, cases one and two can ...