Description

Title: Every graph is (2,3)-choosable

Abstract:

A total weighting of a graph G is a mapping f which assigns to each element

z ∈ V (G)∪E(G) a real number f(z) as its weight. The vertex sum of v

with respect

to f is the sum of weight of v and weights of edges adjacent to v. A

total weighting is proper if vertex sums of adjacent vertices are

distinct. A (k, k')-list assignment is a mapping L which assigns to

each

vertex v a set L(v) of k permissible weights, and assigns to each edge

e a set L(e) of k'

permissible weights. We say G is (k, k')-choosable if for any (k,

k')-list assignment L, there is a proper total weighting f of G with

f(z) ∈ L(z) for each z ∈ V (G)∪E(G).

It was conjectured by Wong and Zhu that every graph is (2,

2)-choosable and every

graph with no isolated edge is (1, 3)-choosable. We will see a proof

of the statement in the title, due to Wong and Zhu.

Abstract:

A total weighting of a graph G is a mapping f which assigns to each element

z ∈ V (G)∪E(G) a real number f(z) as its weight. The vertex sum of v

with respect

to f is the sum of weight of v and weights of edges adjacent to v. A

total weighting is proper if vertex sums of adjacent vertices are

distinct. A (k, k')-list assignment is a mapping L which assigns to

each

vertex v a set L(v) of k permissible weights, and assigns to each edge

e a set L(e) of k'

permissible weights. We say G is (k, k')-choosable if for any (k,

k')-list assignment L, there is a proper total weighting f of G with

f(z) ∈ L(z) for each z ∈ V (G)∪E(G).

It was conjectured by Wong and Zhu that every graph is (2,

2)-choosable and every

graph with no isolated edge is (1, 3)-choosable. We will see a proof

of the statement in the title, due to Wong and Zhu.

Description

Ramanujan Hall

Date

Tue, April 4, 2017

Start Time

11:00am-12:00pm IST

Duration

1 hour

Priority

5-Medium

Access

Public

Created by

DEFAULT ADMINISTRATOR

Updated

Mon, April 3, 2017 10:11am IST