Testing whether there is an induced path in a graph spanning k given vertices is already NP-complete in general graphs when k = 3. We show how to solve this problem in polynomial t...
For any graph G, the k-improper chromatic number k (G) is the smallest number of colours used in a colouring of G such that each colour class induces a subgraph of maximum degree ...
Let k denote the maximum degree of the kth iterated line graph Lk(G). For any connected graph G that is not a path, the inequality k+1 2k - 2 holds. Niepel, Knor, and Solt
In this paper we investigate how graph problems that are NP-hard in general, but polynomially solvable on split graphs, behave on input graphs that are close to being split. For t...
A Shilla distance-regular graph (say with valency k) is a distance-regular graph with diameter 3 such that its second largest eigenvalue equals to a3. We will show that a3 divide...