2 citations · 3 across the 8 of their papers we have counts for
9 papers
The polynomial characterization of tope graphs of the lopsided sets
Xuan Zheng, Yan-Ting Xie, Shou-Jun Xu
The cube polynomial generates the number of -cubes on a graph . As a subclass of partial cubes, the tope graphs of lopsided sets (LOPs) generalize daisy cubes and me…
Cop numbers for subclasses of partial cubes
Zhaoman Huang, Yan-Ting Xie, Shou-Jun Xu
The game of Cops and Robbers is a classical pursuit--evasion game on graphs. For a graph , the cop number is the minimum number of cops needed to guarantee the capture of…
Resolving the Klavžar-Kovše conjecture on opposite semicube isomorphisms in partial cubes and its extension
Zhaoman Huang, Yan-Ting Xie, Shou-Jun Xu
Partial cubes are a fundamental class of graphs that admit isometric embeddings into hypercubes. Klavžar and Kovše [Ars Combin. 93 (2009), 77--86] observed that the opposite semicu…
Resolving problems on polynomial characterizations of daisy cubes and extensions
Xuan Zheng, Yan-Ting Xie, Shou-Jun Xu
Let be a set of binary strings of length . The daisy cube is the subgraph of the hypercube induced by the union of the intervals …
Characterizing simplex graphs
Yan-Ting Xie, Shou-Jun Xu
The simplex graph of a graph is defined as the graph whose vertices are the cliques of (including the empty set), with two vertices being adjacent if, as cliques of…
Ultra log-concavity and real-rootedness of dependence polynomials
Yan-Ting Xie, Shou-Jun Xu
For some positive integer , a real polynomial with is called {log-concave} (resp. ultra log-concave) if $a_k^2\geqslant a_{k-1}…
A relation between the cube polynomials of partial cubes and the clique polynomials of their crossing graphs
Yan-Ting Xie, Yong-De Feng, Shou-Jun Xu
Partial cubes are the graphs which can be embedded into hypercubes. The {\em cube polynomial} of a graph is a counting polynomial of induced hypercubes of , which is defined…
A characterization of regular partial cubes whose all convex cycles have the same lengths
Yan-Ting Xie, Yong-De Feng, Shou-Jun Xu
Partial cubes are graphs that can be isometrically embedded into hypercubes. Convex cycles play an important role in the study of partial cubes. In this paper, we prove that a regu…
Comparability digraphs: An analogue of comparability graphs
Xiao-Lu Gao, Jing Huang, Shou-Jun Xu
Comparability graphs are a popular class of graphs. We introduce as the digraph analogue of comparability graphs the class of comparability digraphs. We show that many concepts suc…