Extremal Graphs without Three-Cycles or Four-Cycles 1 Introduction
Extremal Graphs without Three-Cycles or Four-Cycles. David K. Garnick. Department of Computer Science. Bowdoin College. Brunswick, Maine 04011.
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Extremal Graphs Without 4-Cycles - University of Wyoming
Jan 25, 2012 ... Extremal graph theory officially began with Turán's theorem that solves ... The question of ex(n, C4) (where C4 is a cycle of length 4) has an interesting history; Erd˝os originally ..... This follows from the three previous lemmas. ... [4] Clapham, C. R. J., Flockhart, A., Sheehan, J. Graphs without four-cycles.
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Extremal bipartite graphs with high girth - Departament de
Throughout this paper only undirected simple graphs without loops or multiple edges ... girth of G, g(G) = g, is the length of a shortest cycle in G. Clearly a tree is an acyclic bipartite ..... [5] D.K. Garnick, Y.H.H. Kwong and F. Lazebnik, Extremal graphs without three-cycles or four-cycles, J. Graph Theory 17 (1993), 633–645. 9 ...
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Extremal graphs without three-cycles or four-cycles (PDF
We derive bounds for f (v), the maximum number of edges in a graph on v vertices that contains neither three-cycles nor four-cycles. Also, we give the exact ...
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Sizes of the extremal girth 5 graphs of orders from 40 to 49
Nov 26, 2015 ... The Turán type numbers for graphs without 3-cycles and 4-cycles are determined ... extremal graphs of girth at least five, and in particular their sizes. ...... Thus, ci shares two of its three adjacent G5 components with ci+3, and two with ci−3, ... In particular, each v ∈ V7 has four neighbours in V5, and all its.
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Cycle-maximal triangle-free graphs
Oct 30, 2014 ... Keywords: extremal graph theory, cycle, triangle-free, regular graph, matrix .... graph of girth six or greater, any given cycle can be bridged without creating any triangles. There exist graphs of girth four and five, however, that contain cycles of length .... Three-colourability when δ(G) > 10n/29 follows from the ...
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On the Erd\ H {o} s-Gy\'arf\'as conjecture in claw-free graphs
All graphs in this paper are assumed to be simple, that is, without any loops and. 35 multiple ... we mean a chordless cycle of length at least four. A hole of ... If G is a graph with minimum degree at least three, does G have a cycle whose. 50 ..... [ 5] K. Markström, Extremal graphs for some problems on cycles in graphs,. 206.
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The extremal function for cycles of length l mod k - ETH Zürich
Jun 27, 2016 ... Since the complete bipartite graph Kl−1,n−l+1 has no cycle of length .... graph of minimum degree at least k + 1 contains a cycle of length four modulo k. ..... A bound on the number of edges in graphs without an even cycle, ... [6] G. T. Chen, A. Saito, Graphs with a cycle of length divisible by three, J. Combin.
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Quadrilateral-free graphs with maximum number of - Mathematics
at least 9 0kn{h +|)/ hthen it contains cycles of length 2I for every integer I , k< I ... LetL hbe the graph formed by the lowest three levels of the B oolean lattice Bh ..... YuanshenG and P. Rowlinson , On extremal graphs without four-cycles, U til-.
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Sidon Sets and graphs without 4-cycles
Jan 21, 2014 ... graph that does not contain a 4-cycle has a rich history in extremal graph theory. ... the most studied cases is the Turán number of C4, the cycle on four vertices. ..... Suppose j is a vertex of Gq,θ that is adjacent to three distinct ...
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New Results on EX Graphs | SpringerLink
By the extremal numberex(n; t) = ex(n; {C3, C4, . . . , Ct}) we denote the ... D.K., Kwong Y.H.H., Lazebnik F.: Extremal graphs without three-cycles or four-cycles.
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Small dense subgraphs of polarity graphs and the extremal number
Feb 9, 2015 ... extremal number for the 4-cycle. Michael Tait∗ ... Write Ex(n, F) for the family of n- vertex graphs that are F-free and ... the cycle on four vertices. A well ... a set of q + 1 points, no three of which are collinear. It is known ..... [13] M. Tait, C. Timmons, Sidon sets and graphs without 4-cycles, J. of Combinatorics.,.
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On Hypergraphs of Girth Five∗ 1 Definitions - CiteSeerX
Oct 8, 2002 ... In this paper, we study r-uniform hypergraphs H without cycles of length .... in extremal combinatorics is to prove or disprove that T3(n,4,4) ∼ 5 ... the maximum number of edges in a 3-graph of girth three and four respectively.
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Exact values of ex(ν;{C3,C4,…,Cn})
graph without cycles is said to have an infinite girth. If g(G) = g is ... are the exact values of the corresponding extremal function. Recently in [1] ... The following three inequalities are useful in proving the new results that we have obtained. Since the ..... removal of these four vertices contradicts the assertion that f5(17) = 26.
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Odd cycles and -cycles in hypergraphs
In particular, we address hypergraphs without odd cycles, more generally .... hypergraph is linear if and only if its bigraph is C4-free (has no cycles of length four). .... The three extremal results pertaining to edge-critical bipartite blocks will be ...
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Breaking Symmetries in Graph Representation - IJCAI
“extremal graph theory” [Bollobás, 1978], and its answer is ... without loops or multiple edges. ... Example 1 Figure 1 illustrates three graphs with correspond- ... We use cycle notation to represent permutations. ...... three-cycles or four-cycles.
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References - Sites personnels de TELECOM ParisTech
Jun 14, 2016 ... PUERTAS: Locating-dominating codes: bounds and extremal cardinali- ..... graphs without three-cycles or four-cycles, Journal of Combinatorial.
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Choosability and edge choosability of planar graphs without five
THREE-DEGENERACY Let G be a plane graph without five cycles and 8(G) > 3. .... Since KS is not four choosable, the assumption about five cycles is essential. 3 . .... A.J. Harris, Problems and conjectures in extremal graph theory, Ph.D.
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On the Turán Number for the Hexagon - Princeton University
number of edges in an n-vertex graph without a 2k-gon is asymptotically 1 ... therefore of interest to examine the extremal problem for cycles of length four, .... G contains no cycles of length three, four or six, ω is a walk on a tree T ⊂ G. Now C.
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On the Turán Number for the Hexagon - Microsoft Research
Dec 29, 2003 ... ... for Even Cycles. The problem of determining the extremal number ... A simple construction of graphs without cycles of length exactly 2k, for k ∈ {2,3,5}, ..... T ⊂ G, since G has no cycles of length three, four or six. Therefore T ...
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