Name
Abstract | ||
|---|---|---|
Abstract Given a proper total k -coloring c : V ( G ) ∪ E ( G ) → { 1 , 2 , … , k } of a graph G , we define the value of a vertex v to be c ( v ) + ∑ u v ∈ E ( G ) c ( u v ) . The smallest integer k such that G has a proper total k -coloring whose values form a proper coloring is the neighbor sum distinguishing total chromatic number of G , χ Σ ′ ′ ( G ) . Pilśniak and Woźniak (2013) conjectured that χ Σ ′ ′ ( G ) ≤ Δ ( G ) + 3 for any simple graph with maximum degree Δ ( G ) . In this paper, we prove this bound to be asymptotically correct by showing that χ Σ ′ ′ ( G ) ≤ Δ ( G ) ( 1 + o ( 1 ) ) . The main idea of our argument relies on Przybylo’s proof (2014) regarding neighbor sum distinguishing edge-colorings. |
Year | Venue | Field |
|---|---|---|
2017 | Discrete Mathematics | Integer,Discrete mathematics,Graph,Combinatorics,Vertex (geometry),Degree (graph theory),Sigma,Asymptotically optimal algorithm,Mathematics |
DocType | Volume | Issue |
Journal | 340 | 2 |
Citations | PageRank | References |
1 | 0.37 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sarah Loeb | 1 | 4 | 2.52 |
| yunfang tang | 2 | 1 | 0.37 |