Given a k-arc-strong tournament T , we estimate the minimum number of arcs possible in a k-arc-strong spanning subdigraph of T . We give a construction which shows that for each k ≥ 2 there are tournaments T on n vertices such that every k-arc-strong spanning subdigraph of T contains at least nk+ k(k−1) 2 arcs. In fact, the tournaments in our construction have the property that every spanning s...

An arc in a tournament T with n ≥ 3 vertices is called pancyclic if it belongs to a cycle of length l for all 3 ≤ l ≤ n. We call a vertex u of T an out-arc pancyclic vertex of T if each out-arc of u is pancyclic in T . Yao, Guo and Zhang [Discrete Appl. Math. 99 (2000), 245–249] proved that every strong tournament contains at least one out-arc pancyclic vertex, and they gave an infinite class o...

Let D be a digraph and let λ(D) be the arc-strong connectivity of D, and α′(D) be the size of a maximum matching of D. We proved that if λ(D) ≥ α′(D) > 0, then D has a spanning eulerian subdigraph. C © 2015 Wiley Periodicals, Inc. J. Graph Theory 81: 393–402, 2016

the notion of strong arcs in a fuzzy graph was introduced bybhutani and rosenfeld in [1] and fuzzy end nodes in the subsequent paper[2] using the concept of strong arcs. in mordeson and yao [7], the notion of“degrees” for concepts fuzzified from graph theory were defined and studied.in this note, we discuss degrees for fuzzy end nodes and study further someproperties of fuzzy end nodes and fuzz...

The Path Partition Conjecture for digraphs states that for every digraph D, and every choice of positive integers λ1, λ2 such that λ1 + λ2 equals the order of a longest directed path in D, there exists a partition of D in two subdigraphs D1,D2 such that the order of the longest path in Di is at most λi for i = 1, 2. We present sufficient conditions for a digraph to satisfy the Path Partition Co...