Star chromatic number of triangle-free planar graphs
نویسندگان
چکیده
منابع مشابه
Acyclic chromatic index of triangle-free 1-planar graphs
An acyclic edge coloring of a graph G is a proper edge coloring such that every cycle is colored with at least three colors. The acyclic chromatic index χa(G) of a graph G is the least number of colors in an acyclic edge coloring of G. It was conjectured that χa(G) ≤ ∆(G) + 2 for any simple graph G with maximum degree ∆(G). A graph is 1-planar if it can be drawn on the plane such that every edg...
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More than twenty years ago Erdős conjectured [4] that a triangle-free graph G of chromatic number k ≥ k0(ε) contains cycles of at least k2−ε different lengths as k →∞. In this paper, we prove the stronger fact that every triangle-free graph G of chromatic number k ≥ k0(ε) contains cycles of 1 64 (1− ε)k 2 log k4 consecutive lengths, and a cycle of length at least 14 (1− ε)k 2 log k. As there ex...
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متن کاملOn minimal triangle-free planar graphs with prescribed 1-defective chromatic number
A graph is (m, k)-colourable if its vertices can be coloured with m colours such that the maximum degree of the subgraph induced on the set of all vertices receiving the same colour is at most k. The k-defective chromatic number χk(G) is the least positive integer m for which graph G is (m, k)-colourable. Let f(m, k; planar) be the smallest order of a triangle-free planar graph such that χk(G) ...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 1994
ISSN: 0893-9659
DOI: 10.1016/0893-9659(94)90057-4