Graphs with chromatic number close to maximum degree
نویسندگان
چکیده
منابع مشابه
Graphs with chromatic number close to maximum degree
Let G be a color-critical graph with χ(G) ≥ Δ(G) = 2t + 1 ≥ 5 such that the subgraph of G induced by the vertices of degree 2t+1 has clique number at most t−1. We prove that then either t ≥ 3 and G = K2t+2 or t = 2 and G ∈ {K6, O5}, where O5 is a special graph with χ(O5) = 5 and |O5| = 9. This result for t ≥ 3 improves a case of a theorem by Rabern [9] and for t = 2 answers a question raised by...
متن کاملDistance graphs with maximum chromatic number
Let D be a finite set of integers. The distance graph G(D) has the set of integers as vertices and two vertices at distance d ∈ D are adjacent in G(D). A conjecture of Xuding Zhu states that if the chromatic number of G(D) achieves its maximum value |D| + 1 then the graph has a clique of order |D|. We prove that the chromatic number of a distance graph with D = {a, b, c, d} is five if and only ...
متن کاملThe locating-chromatic number for Halin graphs
Let G be a connected graph. Let f be a proper k -coloring of G and Π = (R_1, R_2, . . . , R_k) bean ordered partition of V (G) into color classes. For any vertex v of G, define the color code c_Π(v) of v with respect to Π to be a k -tuple (d(v, R_1), d(v, R_2), . . . , d(v, R_k)), where d(v, R_i) is the min{d(v, x)|x ∈ R_i}. If distinct vertices have distinct color codes, then we call f a locat...
متن کاملThe chromatic index of graphs with large maximum degree
By Vizing’s theorem, the chromatic index x’(G) of a simple graph G satisfies d(G) Li 1 V(G)1 J + ir, where r is the number of vertices of maximum degree. A graph G is critical if G is Class 2 and x’(H) < x’(G) for all prop...
متن کاملEdge-face chromatic number of plane graphs with high maximum degree
The edge-face chromatic number Xe / (G) of a plane graph G is the smallest number of colors assigned to the edges and faces of G so that any two adjacent or incident elements have different colors. Borodin(1994) proved that L1( G) ~ Xe/ (G) :::; L1( G) + 1 for each plane graph G with ~(G) ~ 10 and the bounds are sharp. The main result of this paper is to give a sufficient and necessary conditio...
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: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2011.12.014