On a constructive characterization of a class of trees related to pairs of disjoint matchings
نویسندگان
چکیده
For a graph consider the pairs of disjoint matchings which union contains as many edges as possible, and define a parameter α which eqauls the cardinality of the largest matching in those pairs. Also, define β to be the cardinality of a maximum matching of the graph. We give a constructive characterization of trees which satisfy the α = β equality. The proof of our main theorem is based on a new decomposition algorithm obtained for trees.
منابع مشابه
Characterization of a class of graphs related to pairs of disjoint matchings
For a given graph consider a pair of disjoint matchings the union of which contains as many edges as possible. Furthermore, consider the ratio of the cardinalities of a maximum matching and the largest matching in those pairs. It is known that for any graph 54 is the tight upper bound for this ratio. We characterize the class of graphs for which it is precisely 5 4 . Our characterization implie...
متن کاملRoman domination excellent graphs: trees
A Roman dominating function (RDF) on a graph $G = (V, E)$ is a labeling $f : V rightarrow {0, 1, 2}$ suchthat every vertex with label $0$ has a neighbor with label $2$. The weight of $f$ is the value $f(V) = Sigma_{vin V} f(v)$The Roman domination number, $gamma_R(G)$, of $G$ is theminimum weight of an RDF on $G$.An RDF of minimum weight is called a $gamma_R$-function.A graph G is said to be $g...
متن کاملA characterization relating domination, semitotal domination and total Roman domination in trees
A total Roman dominating function on a graph $G$ is a function $f: V(G) rightarrow {0,1,2}$ such that for every vertex $vin V(G)$ with $f(v)=0$ there exists a vertex $uin V(G)$ adjacent to $v$ with $f(u)=2$, and the subgraph induced by the set ${xin V(G): f(x)geq 1}$ has no isolated vertices. The total Roman domination number of $G$, denoted $gamma_{tR}(G)$, is the minimum weight $omega(f)=sum_...
متن کاملMultipath Node-Disjoint Routing with Backup List Based on the AODV Protocol
In recent years, routing has been the most focused area in ad hoc networks research. On-demand routing in particular, is widely developed in bandwidth constrained mobile wireless ad hoc networks because of its effectiveness and efficiency. Most proposed on-demand routing protocols are built and relied on single route for each data session. Whenever there is a link disconnection on the active ro...
متن کاملOn trees with equal Roman domination and outer-independent Roman domination numbers
A Roman dominating function (RDF) on a graph $G$ is a function $f : V (G) to {0, 1, 2}$satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least onevertex $v$ for which $f(v) = 2$. A Roman dominating function $f$ is called an outer-independentRoman dominating function (OIRDF) on $G$ if the set ${vin Vmid f(v)=0}$ is independent.The (outer-independent) Roman dom...
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/0708.2363 شماره
صفحات -
تاریخ انتشار 2007