Triangle‐free graphs with large chromatic number and no induced wheel
نویسندگان
چکیده
A wheel is a graph consisting of an induced cycle length at least four and single additional vertex with three neighbours on the cycle. We prove that no Burling contains wheel. graphs are triangle-free have arbitrarily large chromatic number, so this answers question Trotignon disproves conjecture Scott Seymour.
منابع مشابه
On the chromatic number of wheel-free graphs with no large bipartite graphs
A wheel is an induced cycle C plus a vertex connected to at least three vertices of C. Trotignon [14] asked if the class of wheel-free graphs is χ-bounded, i.e. if the chromatic number of every graph with no induced copy of a wheel is bounded by a function of its maximal clique. In this paper, we prove a weaker statement: for every `, the class of graphs with no induced wheel and no induced K`,...
متن کاملInduced subgraphs of graphs with large chromatic number. XI. Orientations
Fix an oriented graph H, and let G be a graph with bounded clique number and very large chromatic number. If we somehow orient its edges, must there be an induced subdigraph isomorphic to H? Kierstead and Rödl [12] raised this question for two specific kinds of digraph H: the three-edge path, with the first and last edges both directed towards the interior; and stars (with many edges directed o...
متن کاملGraphs with Large Distinguishing Chromatic Number
The distinguishing chromatic number χD(G) of a graph G is the minimum number of colours required to properly colour the vertices of G so that the only automorphism of G that preserves colours is the identity. For a graph G of order n, it is clear that 1 6 χD(G) 6 n, and it has been shown that χD(G) = n if and only if G is a complete multipartite graph. This paper characterizes the graphs G of o...
متن کاملGraphs with no induced wheel or antiwheel
A wheel is a graph that consists of a chordless cycle of length at least 4 plus a vertex with at least three neighbors on the cycle. It was shown recently that detecting induced wheels is an NP-complete problem. In contrast, it is shown here that graphs that contain no wheel and no antiwheel have a very simple structure and consequently can be recognized in polynomial time. Four families of gra...
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 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: Journal of Graph Theory
سال: 2022
ISSN: ['0364-9024', '1097-0118']
DOI: https://doi.org/10.1002/jgt.22906