7 papers
Sharp lower bounds for bisections of graphs with bounded maximum degree
Qiwen Guo, Gregory Gutin
A bisection of a graph is a partition of its vertex set into two parts whose sizes differ by at most one. We prove that every graph with edges and maximum degree at most ha…
Bounds on Odd and Odd-Even Induced Subgraphs
Qiwen Guo, Gregory Gutin, Yiming Hao +3
Let be an -vertex graph and let prescribe degree parities. A set is -admissible if every has degree congruent to…
Forward Arc Maximization for Hamilton Oriented Cycles and Paths in Generalizations of Tournaments
Q. Guo, G. Gutin, Y. Lan +3
Gishboliner, Krivelevich, and Michaeli (2023) conjectured the following generalization of Dirac's theorem: If the minimum degree of an -vertex oriented graph is greater…
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…
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…
A new perspective from hypertournaments to tournaments
Jiangdong Ai, Qiming Dai, Qiwen Guo +2
A -tournament on vertices is a pair for , where is a set of vertices, and is a set of all possible -tuples of vertices, such tha…