Nash-Williams' arboricity theorem states that a finite graph is the edge-disjoint union of at most k forests if no set of vertices induces more than k( - 1) edges. We prove a...
In this paper, we consider Steiner forest and its generalizations, prize-collecting Steiner forest and k-Steiner forest, when the vertices of the input graph are points in the Euc...
The vertex colouring problem is known to be NP-complete in the class of triangle-free graphs. Moreover, it remains NP-complete even if we additionally exclude a graph F which is n...
Konrad Dabrowski, Vadim V. Lozin, Rajiv Raman, Ber...
A graphical partition of the even integer n is a partition of n where each part of the partition is the degree of a vertex in a simple graph and the degree sum of the graph is n. ...
Deborah A. Frank, Carla D. Savage, James A. Seller...
We investigate the minimization problem of the minimum degree of minimal Ramsey graphs, initiated by Burr, Erd˝os, and Lov´asz. We determine the corresponding graph parameter fo...