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Order 14 is the largest order for which every 4-total coloring of every cubic graph is equitable
Matheus Adauto, Celina de Figueiredo, Diana Sasaki +1
A total coloring of a graph is an assignment of colors to its vertices and edges so that adjacent or incident elements receive distinct colors, and it is equitable when the cardina…
The sandwich problem for odd-hole-free and even-hole-free graphs
Kathie Cameron, Aristotelis Chaniotis, Celina M. H. de Figueiredo +1
For a property of graphs, the -\textsc{Sandwich-Problem}, introduced by Golumbic and Shamir (1993), is the following: Given a pair of graphs …
An infinite family of Type 1 fullerene nanodiscs
Mariana da Cruz, Diane Castonguay, Celina de Figueiredo +1
A total coloring of a graph colors all its elements, vertices and edges, with no adjacency conflicts. The Total Coloring Conjecture (TCC) is a sixty year old challenge, says that e…
On the pebbling numbers of Flower, Blanuša, and Watkins snarks
Matheus Adauto, Celina de Figueiredo, Glenn Hurlbert +1
Graph pebbling is a game played on graphs with pebbles on their vertices. A pebbling move removes two pebbles from one vertex and places one pebble on an adjacent vertex. The pebbl…