Category Archives: graphs

Partitions of Graphs XI: The Case of all Sufficiently Large n

This the eleventh in a series, the first being found here: Part 1, and the previous here Part 10. In this post I provide examples of Q1 graphs of all orders n, for sufficiently large n.  In particular this will … Continue reading

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Partitions of Graphs X: The Case of Composite Integers

This is the tenth in a series, the first being found here: Part 1, and the previous here: Part 9. In this post I introduce a family of graphs that provides examples of Q1 graphs for all composite orders.  If … Continue reading

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Evening of Math VI

It was late and rushed tonight, but I did manage to do some math with the kids. Actually, A was throwing fits, so I put her to bed. I had B working on the fact that if you have a … Continue reading

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A Morning of Math

I’ve been sick and had to stay home from work the last several days. This morning I told my kids that they could choose to put away their clothes or do math. They chose math. I set both B and … Continue reading

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The Chicken’s Claw

I had my fifth evening of math with my kids.  I got a box of 100 washers from the hardware store and some yarn.  I had the kids draw some graphs and then make some graphs with the washers as … Continue reading

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Partitions of Graphs IX: The case of 13

This is the ninth in a series, the first being here: Part 1, and the previous here: Part 8. Here is a Q1 graph for n=13 o /      o-o-o-o-o-o-o-o-o-o \ o-o The corresponding Q1 partition is 5+5+3.  Unfortunately this … Continue reading

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Partitions of Graphs VIII: The case of 11 (and 17)

This is the eighth in a series, the first being here: Part I and the previous here: Part 7. We have shown that there are no Q1 graphs with n=5 nodes or with n=7 nodes.  Also, in the case of … Continue reading

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