6 papers · 1 filter
A Note on Grünbaum's Conjecture about Longest Cycles and Paths
Masaki Kashima, Kenta Ozeki, Leilei Zhang
Let denote the circumference of a graph , i.e., the number of vertices in its longest cycle. For positive integers and with , let be the cla…
Spanning path-cycle systems with given end-vertices in regular graphs (full version)
Yoshimi Egawa, Mikio Kano, Kenta Ozeki
We prove the following theorem. Let be an integer, and be a -free -edge-connected -regular graph. Then, for every set of even number of vertices of…
A generalization of an ear decomposition and k-trees in highly connected star-free graphs
Shun-ichi Maezawa, Kenta Ozeki, Masaki Yamamoto +1
In this paper, we introduce a generalized version of an ear decomposition, called a -spider decomposition, for -connected star-free graphs with . Its application en…
Odd coloring of -trees
Masaki Kashima, Kenta Ozeki
An odd coloring of a graph is a proper coloring such that every non-isolated vertex has a color that appears at an odd number of its neighbors. This notion was introduced by Petrše…
On odd covers of cliques and disjoint unions
Calum Buchanan, Alexander Clifton, Eric Culver +5
Babai and Frankl posed the ``odd cover problem" of finding the minimum cardinality of a collection of complete bipartite graphs such that every edge of the complete graph of order…
Reconfiguration of Independent Transversals
Pjotr Buys, Ross J. Kang, Kenta Ozeki
Given integers and , suppose there is a graph of maximum degree and a partition of its vertices into blocks of size at least . By a seminal result of Haxel…