2 citations · 3 across the 6 of their papers we have counts for
7 papers · 1 filter
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_…
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…