A note on 3‐partite graphs without 4‐cycles
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DOI: 10.1002/jcd.21742
Abstract: Let C4 be a cycle of order 4. Write ex(n,n,n,C4) for the maximum number of edges in a balanced 3‐partite graph whose vertex set consists of three parts, each has n vertices that have no… read more here.
Keywords: graphs without; note partite; without cycles; partite graphs ... See more keywords
Decomposition of Toroidal Graphs Without Some Subgraphs
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DOI: 10.1007/s40840-023-01631-x
Abstract: We consider a family of toroidal graphs, denoted by $${\mathcal {T}}_{i, j}$$ T i , j , which contain neither i -cycles nor j -cycles. A graph G is ( d , h )-decomposable if… read more here.
Keywords: graphs without; decomposition toroidal; without subgraphs; toroidal graphs ... See more keywords
The Decomposability of Toroidal Graphs without Adjacent Triangles or Short Cycles
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DOI: 10.3390/axioms12020173
Abstract: A graph G has a (d,h)-decomposition if there is a pair (D,F) such that F is a subgraph of G and D is an acyclic orientation of G−E(F), where the maximum degree of F is… read more here.
Keywords: without adjacent; decomposability toroidal; graphs without; toroidal graphs ... See more keywords
Planar Graphs Without 4-Cycles Are (6, 6)-Colorable
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DOI: 10.3390/sym17111865
Abstract: It has been shown that there is a planar graph without 3-cycles which is not (Δ1,Δ2)-colorable for any given Δ1,Δ2. This inspires many research to obtain sufficient conditions for planar graphs without 4-cycles and other… read more here.
Keywords: graphs without; planar graphs; cycles colorable; without cycles ... See more keywords