14 citations · 17 across the 16 of their papers we have counts for
18 papers
Minimal sets for torus homeomorphisms with an irrational circle factor
Xiao-Chuan Liu
We study minimal sets of torus homeomorphisms admitting an irrational circle factor whose fibres are thin essential annular continua. For totally irrational pseudo-rotations and ho…
Strongly separating graph edges with paths
Xiao-Chuan Liu, Boyan Xu, Xu Yang
A family of paths strongly separates the edges of a graph if every two distinct edges are separated in both directions by paths in the family. Bonamy, Botler, Dross, Naia, and Skok…
Sharp Same-Color Cycle Covers in Two-Colored Complete Graphs
Xiao-Chuan Liu, Jonatas Teodomiro, Xu Yang
We extend the conjecture of Erdős and Gyárfás on monochromatic path covers to the setting of monochromatic cycle covers. We prove that, for all , every 2-edge-coloring of the co…
A rainbow version of Lehel's conjecture
Pedro Araújo, Xiao-Chuan Liu, Taísa Martins +4
Lehel's conjecture states that every 2-edge-colouring of K_n admits a partition of its vertex set into two monochromatic cycles. It was proven for sufficiently large n by Łuczak, R…
Linear Lower Bounds for the Modular Chromatic Index
Xiao-Chuan Liu, Boyan Xu, Xu Yang
Let be an integer. A edge-coloring of a graph is an edge-coloring in which every nonzero degree in each color class is congruent to modulo . Let $χ'_…
Large Monochromatic Components in Colored Random Graphs
Xiao-Chuan Liu, Xu Yang
We study the size of the largest monochromatic connected component that must appear in any edge-coloring of a random graph. Let with and , and wri…
On Turán Number of Graphs with Small Minimum Feedback Vertex Numbers
Xiao-Chuan Liu, Xu Yang
Given a graph , the minimum feedback vertex number of is the minimum number of vertices whose removal results in an acyclic graph. In this paper, we investigate Turán-type e…
More on Rainbow Cliques in Edge-Colored Graphs
Xiao-Chuan Liu, Danni Peng, Xu Yang
In an edge-colored graph , a rainbow clique is a -complete subgraph in which all the edges have distinct colors. Let and be the number of edges and colors…
On Non-contractible Periodic Orbits and Bounded Deviations
Xiao-Chuan Liu, Fabio Armando Tal
We present a dichotomy for surface homeomorphisms in the isotopy class of the identity. We show that, in the absence of a degenerate fixed point set, either there exists a uniform…
On Color Isomorphic Pairs in Proper Edge Colourings of Complete Graphs
Xiao-Chuan Liu, Xu Yang
Following the recent paper which initiated the study of colour isomorphism problems for complete graphs, we obtain upper bounds for for a family of graphs obtained a…
Turán Number of Subdivisions of Multipartite Graphs
Xiao-Chuan Liu, Danni Peng, Xu Yang
In this paper, we investigate the Turán exponent for -subdivisions of graphs that are neither bipartite nor complete. Specifically, we establish an upper bound on the Turán numb…
On the Turán Number of Generalized Theta Graphs
Xiao-Chuan Liu, Xu Yang
Let denote the generalized theta graph, which consists of internally disjoint paths with lengths , connecting two fixed vertice…
Uniform convergence rate for Birkhoff means of certain uniquely ergodic toral maps
Silvius Klein, Xiao-Chuan Liu, Aline Melo
We obtain estimates on the uniform convergence rate of the Birkhoff average of a continuous observable over torus translations and affine skew product toral transformations. The co…
Prime Ends Dynamics in Parametrised Families of Rotational Attractors
Jan P. Boroński, Jernej Činč, Xiao-Chuan Liu
We provide several new examples in dynamics on the -sphere, with the emphasis on better understanding the induced boundary dynamics of invariant domains in parametrized families…
On Stable and Unstable Behaviours of Certain Rotation Segments
Salvador Addas-Zanata, Xiao-Chuan Liu
In this paper, we study non-wandering homeomorphisms of the two torus in the identity homotopy class, whose rotation sets are non-trivial line segments from to some totally…
Minimal non-invertible maps on the pseudo-circle
Jan P. Boronski, Judy Kennedy, Xiao-Chuan Liu +1
In this article, we show that R.H. Bing's pseudo-circle admits a minimal non-invertible map. This resolves a problem raised by Bruin, Kolyada and Snoha in the negative. The main to…
Livsic theorem for diffeomorphism cocycles
Artur Avila, Alejandro Kocsard, Xiao-Chuan Liu
We prove the so called Livšic theorem for cocycles taking values in the group of $C^{1+β}-diffeomorphisms of any closed manifold of arbitrary dimension. Since no localization hypot…
On flushed partitions and concave compositions
Xiaochuan Liu
In this work, we give combinatorial proofs for generating functions of two problems, i.e., flushed partitions and concave compositions of even length. We also give combinatorial in…