Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Graph editing problems offer an interesting perspective on sub- and supergraph identification problems for a large variety of target properties. They have also attracted significant attention in recent years, particularly in the area of parameterized complexity as the problems have rich parameter ecologies.#R##N##R##N#  examine generalisations of the notion of editing a graph to obtain a regular subgraph. In particular  extend the notion of regularity to include two variants of edge-regularity along with the unifying constraint of strong regularity.  present a number of results, with the central observation that these problems retain the general complexity profile of their regularity-based inspiration: when the number of edits k and the maximum degree r are taken together as a combined parameter, the problems are tractable (i.e. in FPT), but are otherwise intractable.#R##N##R##N# also examine variants of the basic editing to obtain a regular subgraph problem from the perspective of parameterizing by the treewidth of the input graph. In this case the treewidth of the input graph essentially becomes a limiting parameter on the natural k+rk+r parameterization.
['Luke Mathieson']
I am writing a research paper on a idea Graph editing problems with extended regularity constraints
[{"from": "human", "value": "I am writing a research paper on a idea Graph editing problems with extended regularity constraints"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Graph editing problems offer an interesting perspective on sub- and supergraph identification problems for a large variety of target properties. They have also attracted significant attention in recent years, particularly in the area of parameterized complexity as the problems have rich parameter ecologies.#R##N##R##N#  examine generalisations of the notion of editing a graph to obtain a regular subgraph. In particular  extend the notion of regularity to include two variants of edge-regularity along with the unifying constraint of strong regularity.  present a number of results, with the central observation that these problems retain the general complexity profile of their regularity-based inspiration: when the number of edits k and the maximum degree r are taken together as a combined parameter, the problems are tractable (i.e. in FPT), but are otherwise intractable.#R##N##R##N# also examine variants of the basic editing to obtain a regular subgraph problem from the perspective of parameterizing by the treewidth of the input graph. In this case the treewidth of the input graph essentially becomes a limiting parameter on the natural k+rk+r parameterization."}]