Tag Archives: graph theory

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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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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