2 papers
math.CO2026
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…
math.CO2026
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…