I am about to make a report on the topic of characterization of line graphs then I came across the terms "odd triangles" and "even triangles". Does anyone know what these terms mean?

To elaborate, I am studying the proof of the statement

None of the nine forbidden subgraphs for a line graph $\Rightarrow$ G does not have $K_{1,3}$ as an induced subgraph, and if two triangles have a common line then the subgraph induced by their points is $K_4$". Then, in the proof, it was assumed that G has ODD TRIANGLES $abc$ and $abd$ with $c$ and $d$ not adjacent.

If someone could clarify those terms, he would be a great help in my report.


1 Answer 1


A triangle $\{e_1,e_2,e_3\}⊆V(LG)$ is said to be an odd triangle if there exists a vertex $e∈V(G)$ incident to exactly one or all of $\{e_1,e_2,e_3\}$, and it is said to be even otherwise. [source]


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