Decycling a Graph by the Removal of a Matching: Characterizations for Special Classes
نویسندگان
چکیده
A graph G is matching-decyclable if it has a matching M such that G−M is acyclic. Deciding whether G is matching-decyclable is an NPcomplete problem even if G is 2-connected, planar, and subcubic. In this work we present characterizations of matching-decyclability in the following classes: chordal graphs, split graphs, distance-hereditary graphs, cographs, and Hamiltonian subcubic graphs. All the characterizations lead to simple O(n)-time recognition algorithms.
منابع مشابه
Bounding cochordal cover number of graphs via vertex stretching
It is shown that when a special vertex stretching is applied to a graph, the cochordal cover number of the graph increases exactly by one, as it happens to its induced matching number and (Castelnuovo-Mumford) regularity. As a consequence, it is shown that the induced matching number and cochordal cover number of a special vertex stretching of a graph G are equal provided G is well-covered bipa...
متن کاملOn the decycling number of generalized Kautz digraphs
A set of vertices of a graph whose removal leaves an acyclic graph is called a decycling set of the graph. The minimum size of a decycling set of a graph G is referred to as the decycling number ofG. Let f(d, n) be the decycling number of the generalized Kautz digraph GK(d, n). In this paper, we obtain the upper bound of f(d, n) for all n ≥ d ≥ 2.
متن کاملThe decycling number of graphs
For a graph G and S ⊂ V (G), if G−S is acyclic, then S is said to be a decycling set ofG. The size of a smallest decycling set ofG is called the decycling number of G. The purpose of this paper is a comprehensive review of recent results and several open problems on this graph parameter. Results to be reviewed include recent work on decycling numbers of cubes, grids and snakes(?). A structural ...
متن کاملOn the tenacity of cycle permutation graph
A special class of cubic graphs are the cycle permutation graphs. A cycle permutation graph Pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.In this paper we determine a good upper bound for tenacity of cycle permutation graphs.
متن کاملON THE MATCHING NUMBER OF AN UNCERTAIN GRAPH
Uncertain graphs are employed to describe graph models with indeterministicinformation that produced by human beings. This paper aims to study themaximum matching problem in uncertain graphs.The number of edges of a maximum matching in a graph is called matching numberof the graph. Due to the existence of uncertain edges, the matching number of an uncertain graph is essentially an uncertain var...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1707.02473 شماره
صفحات -
تاریخ انتشار 2017