کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5777666 1632971 2017 29 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Square-free graphs are multiplicative
ترجمه فارسی عنوان
نمودارهای بدون انحنای چندگانه هستند
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
چکیده انگلیسی
A graph K is square-free if it contains no four-cycle as a subgraph (i.e., for every quadruple of vertices, if v0v1,v1v2,v2v3,v3v0∈E(K), then v0=v2 or v1=v3). A graph K is multiplicative if G×H→K implies G→K or H→K, for all graphs G, H. Here G×H is the tensor (or categorical) graph product and G→K denotes the existence of a graph homomorphism from G to K. Hedetniemi's conjecture, which states that χ(G×H)=min⁡(χ(G),χ(H)), is equivalent to the statement that all cliques Kn are multiplicative. However, the only non-trivial graphs known to be multiplicative are K3, odd cycles, and still more generally, circular cliques Kp/q with 2≤pq<4. We make no progress for cliques, but show that all square-free graphs are multiplicative. In particular, this gives the first multiplicative graphs of chromatic number higher than 4. Generalizing, in terms of the box complex, the topological insight behind existing proofs for odd cycles, we also give a different proof for circular cliques with 2≤pq<4.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series B - Volume 122, January 2017, Pages 479-507
نویسندگان
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