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Graph Coloring Methods

graphcoloringmethods.com

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Re: Graph Coloring Methods

#11

Post by siegelzero »

n4r9 wrote: post #2

This looks like a nice book. I took courses in graph theory and ramsey theory at university many years ago. Reading the first couple of pages of the first chapter, it's pitched at a good level for me to jump back into things. Users might find this paragraph from the Preface helpful: > This book is about graph coloring, one of the most popular and widely-studied areas of discrete mathematics. The intended reader is a…

I can recommend the book Guide to Graph Colouring: Algorithms and Applications by Lewis. It covers techniques including some state of the art methods for getting good but not provably optimal colorings. It discusses in depth local search and hybrid evolutionary algorithms, which tend to be the best performing on academic benchmarks (DIMACS graphs and large random graphs).

Re: Graph Coloring Methods

#12

Post by motohagiography »

throwaway290 wrote: post #9
motohagiography wrote: post #8

Earlier quoted context omitted.

it makes more sense in the applications, asking AI, you get examples like how to schedule exams so that no student has a conflict, scheduling flight crews, radio frequency assignment to avoid overlap. e.g. "By representing flights as vertices and connecting edges between flights that share crew members, a coloring algorithm assigns crews to flights to minimize conflicts"

If you think you must ask AI for this, wait till you learn Wikipedia article you replied on says just that but with more sourced detail and less possibility for accidental falsehood

the falsehoods on wikipedia are usually purposeful deceptions so I tend not to bother with it as a go-to. net-net AI has about the same level of accuracy and lacks the actual mendacity.

almost none of us are going to move any discipline forward, let alone discover new math, but as part of the long tail of people who could benefit from recognizing classes of problems with solutions in the domain of graph colouring, AI is sufficient for most purposes.

sorry that nobody appreciates your effort though.

Re: Graph Coloring Methods

#13

Post by generationP »

qwertox wrote: post #4

I was expecting some pretty, colored graphs, but the book is in black and white. From Wikipedia [0]: In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. [0] https://en.wikipedia.org/wiki/Graph_coloring

Lots of academic authors have decided color is a gimmick (color printing is expensive and not clear how long-lived; grayscale printing kills yellow and light-green lines; then there is colorblindness). Certainly I agree that load-bearing color is to be avoided, and I do so in my own writing.

Re: Graph Coloring Methods

#15

Post by throwaway290 »

motohagiography wrote: post #12
throwaway290 wrote: post #9

Earlier quoted context omitted.

If you think you must ask AI for this, wait till you learn Wikipedia article you replied on says just that but with more sourced detail and less possibility for accidental falsehood

the falsehoods on wikipedia are usually purposeful deceptions so I tend not to bother with it as a go-to. net-net AI has about the same level of accuracy and lacks the actual mendacity. almost none of us are going to move any discipline forward, let alone discover new math, but as part of the long tail of people who could benefit from recognizing classes of problems with solutions in the domain of graph colouring, AI…

sorry to break it but AI is nothing but roughly speaking sum / average of data it is fed, if you believe it has some magic layer that excludes mendacity present in that data or in people who select which data to include...

Re: Graph Coloring Methods

#16

Post by rtaylorgarlock »

Daniel is a buddy of mine, and I'm proud of him for self-publishing this. I know 1st hand the crazy amount of hours he put into this over the last 8(?) years. Also relevant to this journey for him is his challenges with his tenured math superiors, leading him to 'leave' the math department for the engineering dept years ago. He chose to self-publish after nearly publishing with one of the math societies, which he's a member of, because he wanted this book to belong to the people doing the work. Big ups to the homie. I'll pass this thread along to him; feedback is appreciated!
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