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Vertex colouring, Edge Colouring, List Colouring, Fractional Chromatic Number and other variants of graph colouring problems are all on topic.
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Graph Coloring: Two adjacent vertices share same color
Consider, subgraphs $G_1, G_2,...... G_x$ of graph $G$. Each subgraph has $k$ vertices.
Now, Fix subgraph $G_1$ and consider another subgraph $G_k$ where $1 <k \le x$.
The edge set between $ …
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Possible Number of Repetation of a Submatrix
Notation:
$H$ is the adjacency matrix of graph $H'$ respectively. $H_k$ is the block or sub-matrix of matrix $H$. The adjacency matrix of graph $H_k \cup H_e$ (subgraphs of $H'$) is $M_{(k,e)}$ wh …