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Two colouring of a 6 by 6 grid without a monochromatic rectangle
WEB2 This question Monochromatic Rectangle of a 2-Colored 8 by 8 Lattice Grid shows that any two colouring of a 7 by 7 grid must have a rectangle whose vertices are all the same colour. Note that we are only considering rectangles whose …
Math.stackexchange.comcombinatorics - Colouring $n$ balls with $k$ colours
WEBJun 2, 2022 · 2 How many ways to colour n n balls with k k colours? Repeating and omitting colours is fine, and order is not important.
Math.stackexchange.comGraph colouring problem - Mathematics Stack Exchange
WEBFeb 21, 2019 · In neither section of the problem are you asked to color the graph. In part a you receive Alice's coloring and you are asked to check whether her claim is correct. That means verifying that no edge of the graph connects two like colored vertices. You are asked to imagine a program that implements that and find how many checks are performed.
Math.stackexchange.comK-tuple colouring in graphs - Mathematics Stack Exchange
WEBI was solving a question related to k-tuple graph colouring. The text states that, A k-tuple colouring of a graph G is an assignment of a set of k different colours to each of the vertices of G suc
Math.stackexchange.comproblem solving - Serious applications of Colouring proofs
WEBApr 14, 2011 · Are there any research-level applications of proofs by colouring? This is the kind of proof you use to show that you can't cover a mutilated chessboard with 31 dominoes. Afaik, this technique chi
Math.stackexchange.comcolouring edges of an icosahedron in a certain way
WEBSep 21, 2020 · Consider the edges of the icosahedron painted red in the following images: You already note that for any coloring of two edges of a face, there are precisely two ways to complete the coloring. For every coloring of the 10 edges indicated in each image, there are only 2 possible colors for some of the edges.
Math.stackexchange.comDefinition of list colouring? - Mathematics Stack Exchange
WEBMar 25, 2020 · A list coloring of a graph is the same thing as a usual vertex coloring, except that instead of having a global set of colors to choose from for each vertex, there is a different list for each vertex. For instance, with K5 K 5, the complete graph on 5 vertices, you can give a proper vertex coloring with colors from {red, blue, black, green
Math.stackexchange.comA question on colouring cubes - Mathematics Stack Exchange
WEBOct 28, 2014 · 1 We are given 6 distinct colours and a cube.We have to colour each face with one of the six colours and two faces with a common edge must be coloured with different colours.How many distinct colouring ways are there?
Math.stackexchange.comEdge-coloring of bipartite graphs - Mathematics Stack Exchange
WEBAny bipartite graph G G has an edge-coloring with Δ(G) Δ (G) (maximal degree) colors. This document proves it on page 4 by: Proving the theorem for regular bipartite graphs; Claiming that if G G bipartite, but not Δ(G) Δ (G) -regular, we can add edges to get a Δ(G) Δ (G) -regular bipartite graph. However, there seem to be two problems
Math.stackexchange.com$K_9$ edge colouring - Mathematics Stack Exchange
WEBJan 26, 2021 · 2 Assume we have K9 K 9 graph and 4 4 colours. We want to colour its edges and obtain following property: If we change colours in our colouring, such graph will be isomorphic to the previous one (before colour change). Moreover, such graph is unique respect to automorphism group. How to do it?
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