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Ricardo Andrade
Ricardo Andrade
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In combinatorics there are very simple basic graphs from which a whole lot of theory came. For example the complete graphs K_5$K_5$ and K_{3,3}$K_{3,3}$ which alone provide the ground level for any non-planar graph according to Kuratowski's theorem. Another simple graph that gave rise to a huge amount of theory is Petersen's graph, which I like to think as the graph whose vertices are the ten two-element subsets of {1,2,3,4,5}$\{1,2,3,4,5\}$, and for which two such vertices are connected iff they are disjoint.

A link for Kuratowski's theorem is http://en.wikipedia.org/wiki/Kuratowski's_theorem

In combinatorics there are very simple basic graphs from which a whole lot of theory came. For example the complete graphs K_5 and K_{3,3} which alone provide the ground level for any non-planar graph according to Kuratowski's theorem. Another simple graph that gave rise to a huge amount of theory is Petersen's graph, which I like to think as the graph whose vertices are the ten two-element subsets of {1,2,3,4,5}, and for which two such vertices are connected iff they are disjoint.

A link for Kuratowski's theorem is http://en.wikipedia.org/wiki/Kuratowski's_theorem

In combinatorics there are very simple basic graphs from which a whole lot of theory came. For example the complete graphs $K_5$ and $K_{3,3}$ which alone provide the ground level for any non-planar graph according to Kuratowski's theorem. Another simple graph that gave rise to a huge amount of theory is Petersen's graph, which I like to think as the graph whose vertices are the ten two-element subsets of $\{1,2,3,4,5\}$, and for which two such vertices are connected iff they are disjoint.

A link for Kuratowski's theorem is http://en.wikipedia.org/wiki/Kuratowski's_theorem

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Vania Mascioni
Vania Mascioni
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In combinatorics there are very simple basic graphs from which a whole lot of theory came. For example the complete graphs K_5 and K_{3,3} which alone provide the ground level for any non-planar graph according to Kuratowski's theorem. Another simple graph that gave rise to a huge amount of theory is Petersen's graph, which I like to think as the graph whose vertices are the eight binary triplesten two-element subsets of (with entries 0 or 1){1,2,3,4,5}, and for which two such vertices are connected iff the associated triples have Hamming distance 1they are disjoint.

A link for Kuratowski's theorem is http://en.wikipedia.org/wiki/Kuratowski's_theorem

In combinatorics there are very simple basic graphs from which a whole lot of theory came. For example the complete graphs K_5 and K_{3,3} which alone provide the ground level for any non-planar graph according to Kuratowski's theorem. Another simple graph that gave rise to a huge amount of theory is Petersen's graph, which I like to think as the graph whose vertices are the eight binary triples (with entries 0 or 1), and for which two such vertices are connected iff the associated triples have Hamming distance 1.

A link for Kuratowski's theorem is http://en.wikipedia.org/wiki/Kuratowski's_theorem

In combinatorics there are very simple basic graphs from which a whole lot of theory came. For example the complete graphs K_5 and K_{3,3} which alone provide the ground level for any non-planar graph according to Kuratowski's theorem. Another simple graph that gave rise to a huge amount of theory is Petersen's graph, which I like to think as the graph whose vertices are the ten two-element subsets of {1,2,3,4,5}, and for which two such vertices are connected iff they are disjoint.

A link for Kuratowski's theorem is http://en.wikipedia.org/wiki/Kuratowski's_theorem

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Vania Mascioni
Vania Mascioni
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In combinatorics there are very simple basic graphs from which a whole lot of theory came. For example the complete graphs K_5 and K_{3,3} which alone provide the ground level for any non-planar graph according to Kuratowski's theorem. Another simple graph that gave rise to a huge amount of theory is Petersen's graph, which I like to think as the graph whose vertices are the eight binary triples (with entries 0 or 1), and for which two such vertices are connected iff the associated triples have Hamming distance 1.

A link for Kuratowski's theorem is http://en.wikipedia.org/wiki/Kuratowski's_theorem