2 citations · 3 across the 8 of their papers we have counts for
4 papers · 1 filter
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 …