5 papers
A Sublinear Minimum-Degree Condition for -Connected Subgraphs of All Orders
Kenta Ozeki, Takahiro Ueoro
Motivated by an analogue of pancyclicity, we study minimum-degree conditions ensuring that a -connected graph of order contains a -connected subgraph of every order $…
Cover numbers by graph families bounded by certain graph parameters
Anna Gujgiczer, Márton Marits, Kenta Ozeki
The cover number of a graph by a graph class is the least number of -graphs necessary to cover its edges. A classical theorem of Harary, Hsu and Miller giv…
The square of a subcubic planar graph without a 5-cycle is 7-choosable
Seog-Jin Kim, Xiaopan Lian, Atsuhiro Nakamoto +1
The square of a graph , denoted , has the same vertex set as and has an edge between two vertices if the distance between them in is at most . Thomassen [12] sho…
Minors of non-hamiltonian polyhedra and the Herschel family
On-Hei Solomon Lo, Kenta Ozeki
We show that every non-hamiltonian polyhedron contains the Herschel graph as a minor, implying that the Herschel graph is the unique minor-minimal non-hamiltonian polyhedron. Our a…
Colouring normal quadrangulations of projective spaces
Tomáš Kaiser, On-Hei Solomon Lo, Atsuhiro Nakamoto +2
Youngs proved that every non-bipartite quadrangulation of the projective plane is 4-chromatic. Kaiser and Stehl\'ık [J. Combin. Theory Ser. B 113 (2015), 1…