1 citations · 1 across the 20 of their papers we have counts for
21 papers · 1 filter
The asymptotic maximum oriented diameter of graphs
Jiangdong Ai, Yaokun Feng, Hui Lei +1
The oriented diameter of a connected bridgeless graph is the minimum diameter of a strong orientation. Let be the maximum oriented diameter among all such graphs of diameter…
A linear bound for nested cycles without geometric crossings
Jiangdong Ai, Gregory Gutin, Yiming Hao
Cycles in a graph are called nested without geometric crossings if they are pairwise edge-disjoint, , and each pair of conse…
Improved Bounds for Unavoidable Claws in Tournaments
Jiangdong Ai, Yongxin Lan
Let be the largest integer such that every -vertex claw with at most branches occurs in every tournament on vertices, and let $c_{\mathrm{claw}}=\limsup_{n\to…
Finite palette endpoints and degree-square Turán problems
Jiangdong Ai, Bin Chen, Ming Chen +2
We study finite palette extremal problems motivated by uniform Turán densities of -uniform hypergraphs. Given a self-converse tournament with at least two vertices, we deter…
Quasi-kernels in Hereditary Classes and Applications to Break
Jiangdong Ai, Tianyu Huang, Xiangzhou Liu +2
Recently, Nguyen, Seymour and Scott verified the small quasi-kernel conjecture for split digraphs, and initiated the study of quasi-kernels in break digraphs. Following their resea…
A quadratic refinement of Jackson's \CE\ condition for Hamilton cycles in digraphs
Jiangdong Ai, Yongtang Shi
For a digraph , let be the largest size of a vertex set no two of whose vertices lie in a common directed -cycle. Let be the least integer such that eve…
A weighted cycle-localization inequality
Jiangdong Ai, Bin Chen, Ming Chen +1
In 1959, Erdős and Gallai showed that every -connected graph contains a cycle of length at least . This result was subsequently extended to weighte…
Feedback vertex sets of digraphs with bounded maximum degree
Jiangdong Ai, Gregory Gutin, Xiangzhou Liu +2
A digraph is an oriented graph if does not have a pair of opposite arcs. The degree of a vertex of is the sum of the in-degree and out-degree of Let b…
Odd Induced Subgraphs in Graphs of Maximum Degree Four
Jiangdong Ai, Qiwen Guo, Gregory Gutin +2
A graph is called odd if all of its vertex degrees are odd. A long-standing conjecture asked whether there exists a positive constant such that every -vertex graph without i…
Note on Long Directed Cycles in Eulerian Digraphs
Jiangdong Ai, Gregory Gutin, Fankang He +1
Huang, Ma, Shapira, Sudakov and Yuster (Comb. Prob. Comput. 2013) proved that every Eulerian digraph of average out-degree has a directed cycle of length at least W…
Large induced subgraphs with prescribed degree parity
Jiangdong Ai, Qiwen Guo, Gregory Gutin +2
A long-standing conjecture of Caro (Discrete Math, 1994), confirmed by Ferber and Krivelevich (Adv Math, 2022), states that every -vertex graph without isolated vertices con…
Oriented discrepancy of Hamilton cycles in oriented graphs satisfying Ore-type condition
Jiangdong Ai, Qiwen Guo, Gregory Gutin +4
Erd{\H o}s (1963) initiated extensive graph discrepancy research on 2-edge-colored graphs. Gishboliner, Krivelevich, and Michaeli (2023) launched similar research on oriented graph…
Number of Subgraphs and Their Converses in Tournaments and New Digraph Polynomials
Jiangdong Ai, Gregory Gutin, Hui Lei +2
An oriented graph is converse invariant if, for any tournament , the number of copies of in is equal to that of its converse . El Sahili and Ghazo Hanna [J. Grap…
On Seymour's and Sullivan's Second Neighbourhood Conjectures
Jiangdong Ai, Stefanie Gerke, Gregory Gutin +3
For a vertex of a digraph, (, resp.) is the number of vertices at distance 1 from (to, resp.) and is the number of vertices at distance 2 from…
Bounds on Maximum Weight Directed Cut
Jiangdong Ai, Stefanie Gerke, Gregory Gutin +2
We obtain lower and upper bounds for the maximum weight of a directed cut in the classes of weighted digraphs and weighted acyclic digraphs as well as in some of their subclasses.…
Results on the Small Quasi-Kernel Conjecture
Jiangdong Ai, Stefanie Gerke, Gregory Gutin +2
A {\em quasi-kernel} of a digraph is an independent set such that for every vertex , there exists a directed path with one or two arcs…
Extended Path Partition Conjecture for Semicomplete and Acyclic Compositions
Jiangdong Ai, Stefanie Gerke, Gregory Gutin +1
Let be a digraph and let denote the number of vertices in a longest path of . For a pair of vertex-disjoint induced subdigraphs and of , we say that $(A,B)…
Kings in Multipartite Hypertournaments
Jiangdong Ai, Stefanie Gerke, Gregory Gutin
In his paper "Kings in Bipartite Hypertournaments" (Graphs Combinatorics 35, 2019), Petrovic stated two conjectures on 4-kings in multipartite hypertournaments. We prove one o…
Proximity and Remoteness in Directed and Undirected Graphs
Jiangdong Ai, Stefanie Gerke, Gregory Gutin +1
Let be a strongly connected digraph. The average distance of a vertex of is the arithmetic mean of the distances from to all other vertices of . The r…
Proper Orientation Number of Triangle-free Bridgeless Outerplanar Graphs
J. Ai, S. Gerke, G. Gutin +2
An orientation of is a digraph obtained from by replacing each edge by exactly one of two possible arcs with the same endpoints. We call an orientation \emph{proper} if nei…
k-Ary spanning trees contained in tournaments
Jiangdong Ai, Hui Lei, Yongtang Shi +2
A rooted tree is called a -ary tree, if all non-leaf vertices have exactly children, except possibly one non-leaf vertex has at most children. Denote by the min…