This is the final part of the graph theory notes. We take a look at Tournaments. Tournaments So far all the graphs encountered were undirected that is, none of the edges that stood for “relationship” between two vertex had any direction. If we attach some directional information to an edge, then the graph is called a directed graph. Let the directional information be represented by an arrow which points to a vertex from another vertex, the from side has the arrow and is called an arc in literature.

This is the seventh part of the graph theory notes. We take a look at Planar Graphs. The book followed throughout is: Graph Theory with Applications by Bondy J.A., Murty U.S.R.. Please refer to the book for examples as well as visual graph drawings. Planar Graphs A graph is called Planar if it can be drawn in the plane so that its edges intersect only at their ends. The vertices and edges of the graph partition (no overlap) the plane into several regions, each such region is called a face, denoted by $F_i$ for some $i \in \mathbb{N}$.

This is the eight part of the graph theory notes. We take a look at some theorems mostly related to Ramsey Numbers. The book followed for the other notes is : Graph Theory with Applications by Bondy J.A., Murty U.S.R.. Please refer to the book for examples as well as visual graph drawings. For this post, the readers are also encouraged to seek the proofs in other books such as the legendary Adrian Bondy & U.

This is the sixth part of the graph theory notes. We take a look at Hamiltonian Graphs. We omit a tactics section since the questions related to Hamiltonian Graphs are diverse each requiring some approach unique in its own way, please see the #Questions section for further references. The book followed throughout is: Graph Theory with Applications by Bondy J.A., Murty U.S.R.. Please refer to the book for examples as well as visual graph drawings.

This is the fifth part of the graph theory notes. We take a look at Euler’s Problem and its resolution in this post. The book followed throughout is: Graph Theory with Applications by Bondy J.A., Murty U.S.R.. Please refer to the book for examples as well as visual graph drawings. Regarding the Königsberg Problem The entirety of the Königsberg problem solved by Euler is covered at various places; Please refer to here - for a audiovisual treatment or here - for a full report on it.