A Brooks-Type Result for Sparse Critical Graphs
نویسندگان
چکیده
منابع مشابه
On Brooks' Theorem for Sparse Graphs
Let G be a graph with maximum degree ∆(G). In this paper we prove that if the girth g(G) of G is greater than 4 then its chromatic number, χ(G), satisfies χ(G) ≤ (1 + o(1)) ∆(G) log ∆(G) where o(1) goes to zero as ∆(G) goes to infinity. (Our logarithms are base e.) More generally, we prove the same bound for the list-chromatic (or choice) number: χ l (G) ≤ (1 + o(1)) ∆(G) log ∆(G) provided g(G)...
متن کاملA Brooks-type Theorem for the Bandwidth of Interval Graphs
Let G be an interval graph. The layout that arranges the intervals in order by right endpoint easily shows that the bandwidth of G is at most its maximum degree ∆. Hence, if G contains a clique of size ∆ + 1, then its bandwidth must be ∆. In this paper we prove a Brooks-type bound on the bandwidth of interval graphs. Namely, the bandwidth of an interval graph is at most ∆, with equality if and ...
متن کاملA generalization of Villarreal's result for unmixed tripartite graphs
In this paper we give a characterization of unmixed tripartite graphs under certain conditions which is a generalization of a result of Villarreal on bipartite graphs. For bipartite graphs two different characterizations were given by Ravindra and Villarreal. We show that these two characterizations imply each other.
متن کاملA Brooks' Theorem for Triangle-Free Graphs
Let G be a triangle-free graph with maximum degree ∆(G). We show that the chromatic number χ(G) is less than 67(1 + o(1))∆/ log∆.
متن کاملA matroid analogue of a theorem of Brooks for graphs
Brooks proved that the chromatic number of a loopless connected graph G is at most the maximum degree of G unless G is an odd cycle or a clique. This note proves an analogue of this theorem for GF (p)-representable matroids when p is prime, thereby verifying a natural generalization of a conjecture of Peter Nelson.
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: Combinatorica
سال: 2018
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-017-3068-3