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20 votes
Accepted

Content for a 40-minute lecture on graph theory for high schoolers

I suggest you discuss the Seven bridges of Königsberg problem (the problem that essentially started the field of graph theory), then discuss the Three utilities problem. For each, discuss the problem ...
JRN's user avatar
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12 votes

Content for a 40-minute lecture on graph theory for high schoolers

I study pursuit-evasion games on graphs, so I will recommend using the cops & robbers game as a way to introduce graph theoretic terminology, concepts, and examples. It should also keep the tone ...
Brendan W. Sullivan's user avatar
6 votes

Content for a 40-minute lecture on graph theory for high schoolers

I would try to keep it heavy on sugar and light on medicine. In particular emphasize visual representations more than precise terms that students don't know (or even worse, symbol soup). Maybe ...
gues's user avatar
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5 votes

Content for a 40-minute lecture on graph theory for high schoolers

I always introduce graph theory with the Königsberg Bridges, as Joel Reyes Noche suggested in his answer. Years ago, I went to a wonderful math talk that used this problem to describe 5 or more ...
Sue VanHattum's user avatar
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5 votes

What are standard (or good) textbooks for undergraduate graph theory?

I use "Introductory Graph Theory" by Gary Chartrand (Dover, 1985) because it is heavy on applications and introduces some of the concepts only after presenting examples that would need them. (A ...
JRN's user avatar
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5 votes

Content for a 40-minute lecture on graph theory for high schoolers

You might include results on coloring plane graphs: The Art Gallery Theorem: $3$-coloring. Using Euler's theorem to prove that there must be a vertex of degree at most $5$. From there to $6$-coloring ...
Joseph O'Rourke's user avatar
4 votes
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Is there any video lecture series on Graph Theory which uses "Introduction to Graph Theory" by Douglas West? as the text

The Canvas class for Dartmouth's Spring 2020 course in Graph Theory, Math 38, seems to be mostly open. According to the syllabus, the course uses the 2nd edition of West's Introduction to Graph Theory....
shoover's user avatar
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3 votes

Is "The Petersen Graph" by Holton and Sheehan a good text for graph-theory students? Any requisite knowledge for mastering the text?

There are no Amazon reviews. Doesn't seem like a popular title. (Just an indicator, not a Euclidean proof...but a negative note.) The preface says that it is approaching teaching all of graph theory ...
guest's user avatar
  • 31
3 votes

Content for a 40-minute lecture on graph theory for high schoolers

Here's a drawing of a house Can you draw it without lifting your pencil? What about if the roof is removed? What about two houses side-to-side? Here’s the floor plan for a house with some doors (...
BlueRaja - Danny Pflughoeft's user avatar
2 votes
Accepted

Start drawing a graph

There is quite a bit of literature on this topic in the "Graph Drawing" community. Although the goal is algorithms for automatically drawing graphs, several papers offer criteria which could ...
Joseph O'Rourke's user avatar
2 votes

Content for a 40-minute lecture on graph theory for high schoolers

Typical topics are the Dijkstra and Floyd algorithms to find the shortest way between two nodes in a graph (used e.g. for NPC wayfinding in games, navigation etc.) or typical problems of IT theory (e....
Sprinklerkopf's user avatar
2 votes

What are some decent apps for Hasse diagrams?

This is such a niche request that I doubt you're going to be able to find an off-the-shelf app that does everything you want (though I'd love to be proven wrong). That said, Mathematica has a ...
Justin Skycak's user avatar
1 vote

What are some decent apps for Hasse diagrams?

You may want to use Sage. Sage is a mathematics toolkit built upon Python and is extremely powerful, if occasionally slow due to its generality. The documentation of Hasse diagrams doesn't include how ...
Opal E's user avatar
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1 vote

An intuitive (non rigorous) text book on graph theory which is student friendly with vivid illustrations

That book gets ripped pretty hard on Amazon. The Dover texts by Trudeau and Chartrand are supposedly easier and friendlier, per reviews. And will be cheap, since Dover. If you want to develop ...
guest's user avatar
  • 151
1 vote

What are standard (or good) textbooks for undergraduate graph theory?

For completeness, I do recommend several "Moore method"/inquiry-based sets of notes found at the Journal of Inquiry-Based Learning in Mathematics website. I have successfully used a pastiche of these ...
kcrisman's user avatar
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