Edge shift distance between trees
Edge shift distance between isomorphism classes of graphs, introduced by M. Johnson, is investigated in the case of trees and compared with other distances.
Edge shift distance between isomorphism classes of graphs, introduced by M. Johnson, is investigated in the case of trees and compared with other distances.
Edge-colourings of graphs have been studied for decades. We study edge-colourings with respect to hereditary graph properties. For a graph , a hereditary graph property and we define to be the minimum number of colours needed to properly colour the edges of , such that any subgraph of induced by edges coloured by (at most) colours is in . We present a necessary and sufficient condition for the existence of . We focus on edge-colourings of graphs with respect to the hereditary properties...
The edge-domatic number of a graph is the maximum number of classes of a partition of its edge set into dominating sets. This number is studied for cacti, i.e. graphs in which each edge belongs to at most one circuit.
In this paper, we investigate a measure of similarity of graphs similar to the Ramsey number. We present values and bounds for , the biggest number guaranteeing that there exist graphs on vertices, each two having edit distance at least . By edit distance of two graphs , we mean the number of edges needed to be added to or deleted from graph to obtain graph . This new extremal number is closely linked to the edit distance of graphs. Using probabilistic methods we show that is close...