منابع مشابه
Equitable List Coloring of Graphs
A graph G is equitably k-choosable if, for any k-uniform list assignment L, G admits a proper coloring π such that π(v) ∈ L(v) for all v ∈ V (G) and each color appears on at most |G|/k vertices. It was conjectured in [8] that every graph G with maximum degree ∆ is equitably k-choosable whenever k ≥ ∆ + 1. We prove the conjecture for the following cases: (i) ∆ ≤ 3; (ii) k ≥ (∆ − 1). Moreover, eq...
متن کاملA list analogue of equitable coloring
Given lists of available colors assigned to the vertices of a graph G, a list coloring is a proper coloring of G such that the color on each vertex is chosen from its list. If the lists all have size k, then a list coloring is equitable if each color appears on at most dn(G )/ke vertices. A graph is equitably k-choosable if such a coloring exists whenever the lists all have size k. We prove tha...
متن کاملEquitable List Coloring of Graphs with Bounded Degree
A graph G is equitably k-choosable if for every k-list assignment L there exists an L-coloring of G such that every color class has at most d|G|/ke vertices. We prove results towards the conjecture that every graph with maximum degree at most r is equitably (r+1)choosable. In particular, we con rm the conjecture for r ≤ 7 and show that every graph with maximum degree at most r and at least r ve...
متن کاملList total coloring of pseudo-outerplanar graphs
A graph is pseudo-outerplanar if each of its blocks has an embedding in the plane so that the vertices lie on a fixed circle and the edges lie inside the disk of this circle with each of them crossing at most one another. It is proved that every pseudo-outerplanar graph with maximum degree ∆ ≥ 5 is totally (∆ + 1)-choosable.
متن کاملEquitable total coloring of corona of cubic graphs
The minimum number of total independent sets of V ∪ E of graph G(V,E) is called the total chromatic number of G, denoted by χ′′(G). If difference of cardinalities of any two total independent sets is at most one, then the minimum number of total independent partition sets of V ∪E is called the equitable total chromatic number, and denoted by χ′′ =(G). In this paper we consider equitable total c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2018
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-018-1965-x