Rosenfeld, Moshe

Hamilton decomposition of prisms over 3-connected cubic planar graphs ★★

Author(s): Alspach; Rosenfeld

Conjecture   Every prism over a -connected cubic planar graph can be decomposed into two Hamilton cycles.

Keywords:

Every prism over a 3-connected planar graph is hamiltonian. ★★

Author(s): Kaiser; Král; Rosenfeld; Ryjácek; Voss

Conjecture   If is a -connected planar graph, then has a Hamilton cycle.

Keywords:

A gold-grabbing game ★★

Author(s): Rosenfeld

Setup Fix a tree and for every vertex a non-negative integer which we think of as the amount of gold at .

2-Player game Players alternate turns. On each turn, a player chooses a leaf vertex of the tree, takes the gold at this vertex, and then deletes . The game ends when the tree is empty, and the winner is the player who has accumulated the most gold.

Problem   Find optimal strategies for the players.

Keywords: game; tree

Coloring the Odd Distance Graph ★★★

Author(s): Rosenfeld

The Odd Distance Graph, denoted , is the graph with vertex set and two points adjacent if the distance between them is an odd integer.

Question   Is ?

Keywords: coloring; geometric graph; odd distance

A generalization of Vizing's Theorem? ★★

Author(s): Rosenfeld

Conjecture   Let be a simple -uniform hypergraph, and assume that every set of points is contained in at most edges. Then there exists an -edge-coloring so that any two edges which share vertices have distinct colors.

Keywords: edge-coloring; hypergraph; Vizing 