Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract#R##N##R##N#  prove the following theorem: Let D be a k-arcconnected digraph (multiple arcs allod). If x is a vertex of D and / is an integer with / ≤ k, then for any / disjoint arc pairs {f1, g1}, ⃛, {f1, g1}, where f1, ⃛, f1 are arcs with head at x and g1, ⃛, g1 are arcs with tail at x, there exist in D / arc-disjoint cycles C1, ⃛, C1 such that {fi, gi} ⊆ E(Ci) for each i (E(Ci) denotes the arc set of Ci) and such that D - ∪ E(Ci) is (k - 1)-arc-connected. Several interesting results are deduced from this theorem. Our results generalize the early works of Mader (“On a Property of n-Edge-Connected Digraphs,” Combinatorica, vol. 1 [1981], pp. 385-386) and Shiloach (“Edge-Disjoint Branching in Directed Multigraphs,” Information Processing Letters, vol. 8 [1979], pp. 24-27). An extension of Mader's theorem about admissible liftings of digraphs is also obtained in this paper. © 1995 John Wiley & Sons, Inc.
['Xiang-Ying Su']
I am writing a research paper on a idea Paths, cycles, and arc-connectivity in digraphs
[{"from": "human", "value": "I am writing a research paper on a idea Paths, cycles, and arc-connectivity in digraphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract#R##N##R##N#  prove the following theorem: Let D be a k-arcconnected digraph (multiple arcs allod). If x is a vertex of D and / is an integer with / \u2264 k, then for any / disjoint arc pairs {f1, g1}, \u20db, {f1, g1}, where f1, \u20db, f1 are arcs with head at x and g1, \u20db, g1 are arcs with tail at x, there exist in D / arc-disjoint cycles C1, \u20db, C1 such that {fi, gi} \u2286 E(Ci) for each i (E(Ci) denotes the arc set of Ci) and such that D - \u222a E(Ci) is (k - 1)-arc-connected. Several interesting results are deduced from this theorem. Our results generalize the early works of Mader (\u201cOn a Property of n-Edge-Connected Digraphs,\u201d Combinatorica, vol. 1 [1981], pp. 385-386) and Shiloach (\u201cEdge-Disjoint Branching in Directed Multigraphs,\u201d Information Processing Letters, vol. 8 [1979], pp. 24-27). An extension of Mader's theorem about admissible liftings of digraphs is also obtained in this paper. \u00a9 1995 John Wiley & Sons, Inc."}]