Noah Prince

• Discrete Mathematics
• 2008
Let D(H) be the minimum d such that every graph G with average degree d has an H-minor. Myers and Thomason found good bounds onD(H) for almost all graphsH and proved that for â€˜balancedâ€™H randomâ€¦ (More)
• 5
• Discrete Mathematics
• 2009
ErdÅ‘s and LovÃ¡sz conjectured in 1968 that for every graph G with Ï‡(G) > Ï‰(G) and any two integers s, t â‰¥ 2 with s + t = Ï‡(G) + 1, there is a partition (S, T ) of the vertex set V (G) such thatâ€¦ (More)
• 4
• 4
• SIAM J. Discrete Math.
• 2009
A Roman dominating function of a graph G is a labeling f : V (G) â†’ {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2. The Roman domination number Î³R(G) of G is the minimum ofâ€¦ (More)
• 4
• Discrete Mathematics
• 2010
Let K âˆ— 3,t denote the graph obtained from K3,t by adding all edges between the three vertices of degree t in it. We prove that for each t â‰¥ 6300 and n â‰¥ t + 3, each n-vertex graph G with e(G) > 1 2â€¦ (More)
• 4
• Discrete Mathematics
• 2012
Let Kâˆ— s,t denote the graph obtained from Ks,t by adding all edges between the s vertices of degree t in it. We show how to adapt the argument of an our previous paper (Discrete Math. 308 (2008),â€¦ (More)
• 3
• SIAM J. Discrete Math.
• 2013
Let G be a weighted graph in which each vertex initially has weight 1. A total acquisition move transfers all the weight from a vertex u to a neighboring vertex v, under the condition that before theâ€¦ (More)
• Graphs and Combinatorics
• 2009
Define a k-minimum-difference-representation (k-MDR) of a graph G to be a family of sets {S(v) : v âˆˆ V (G)} such that u and v are adjacent in G if and only if min{|S(u)âˆ’ S(v)|, |S(v)âˆ’ S(u)|} â‰¥ k.â€¦ (More)