Tag 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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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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Partitions of Graphs VII: The Cases of 5 and 7

This is the seventh in a series, the first being here: Part I, the previous here: Part VI. In the previous post I defined a Q1 graph to be a graph G with q(G)=1.  We found examples of Q1 graphs … Continue reading

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Partitions of Graphs VI: Q1 Graphs

This is the sixth in a series.  The first is found here: Part I.  The previous is found here: Part V. I have defined q(G) to be: q(G) = p(n) – p(G), where n is the number of nodes in G. … Continue reading

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Partitions of Graphs V: Some Examples

This is the fifth in a series.  See the first here: Part I, and the previous here: Part IV. In my last post I said what I mean by p(G), when G is a graph.  Namely, it is the number … Continue reading

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Partitions of Graphs III: Ramanujan meets Kevin Bacon

This is the third in a series (see also Partitions of Graphs I and Partitions of Graphs II). Chances are you’ve played with graphs before.  If you’ve ever played the Kevin Bacon game, you’ve played with graphs.  The game goes … Continue reading

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Proof of radlam Classification

Enough talk, let’s do some math. Sketch of proof of the classification theorem given in The Graph Type of a Polyomino. (I defined radlams in the post Raldams.): First we need some lemmas on how radlams decompose. Lemma 1 (the … Continue reading

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The Graph type of a Polyomino

This is a continuation of the post radlams. A graph is some dots (called nodes or vertices) and lines between some of them (called edges). It’s not the geometry of the graph that matters, just how the vertices are connected … Continue reading

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