scholarly journals On the number of linear hypergraphs of large girth

2019 ◽  
Vol 93 (1) ◽  
pp. 113-141
Author(s):  
József Balogh ◽  
Lina Li
Keyword(s):  
Large Girth ◽  
Linear Hypergraphs

Cubic Graphs with Large Girth

1989 ◽  
Vol 555 (1 Combinatorial) ◽  
pp. 56-62 ◽  
Author(s):  
N. L. BIGGS
Keyword(s):  
Cubic Graphs ◽  
Large Girth

scholarly journals Intersection Graphs of k-uniform Linear Hypergraphs

1982 ◽  
Vol 3 (2) ◽  
pp. 159-172 ◽  
Author(s):  
Ranjan N. Naik ◽  
S.B. Rao ◽  
S.S. Shrikhande ◽  
N.M. Singhi
Keyword(s):  
Intersection Graphs ◽  
Linear Hypergraphs

Uniquely Colourable Graphs with Large Girth

1976 ◽  
Vol 28 (6) ◽  
pp. 1340-1344 ◽  
Author(s):  
Béla Bollobás ◽  
Norbert Sauer
Keyword(s):  
Chromatic Number ◽  
Large Girth ◽  
Large Chromatic Number

Tutte [1], writing under a pseudonym, was the first to prove that a graph with a large chromatic number need not contain a triangle. The result was rediscovered by Zykov [5] and Mycielski [4]. Erdös [2] proved the much stronger result that for every k ≧ 2 and g there exist a k-chromatic graph whose girth is at least g.

scholarly journals Light graphs in planar graphs of large girth

2016 ◽  
Vol 36 (1) ◽  
pp. 227
Author(s):  
Peter Hudák ◽  
Mária Maceková ◽  
Tomas Madaras ◽  
Pavol Široczki
Keyword(s):  
Planar Graphs ◽  
Large Girth

scholarly journals Some Results on Chromaticity of Quasi-Linear Paths and Cycles

10.37236/2370 ◽  
2012 ◽  
Vol 19 (2) ◽  
Author(s):  
Ioan Tomescu
Keyword(s):  
Linear Hypergraphs

Let $r\geq 1$ be an integer. An $h$-hypergraph $H$ is said to be $r$-quasi-linear (linear for $r=1$) if any two edges of $H$ intersect in 0 or $r$ vertices. In this paper it is shown that $r$-quasi-linear paths $P_{m}^{h,r}$ of length $m\geq 1$ and cycles $C_{m}^{h,r}$ of length $m\geq 3$ are chromatically unique in the set of $h$-uniform $r$-quasi-linear hypergraphs provided $r\geq 2$ and $h\geq 3r-1$. 

Constructive Packings by Linear Hypergraphs

2013 ◽  
Vol 22 (6) ◽  
pp. 829-858 ◽  
Author(s):  
JILL DIZONA ◽  
BRENDAN NAGLE
Keyword(s):  
Maximum Size ◽  
Np Hard ◽  
Edge Disjoint ◽  
Analogous Algorithm ◽  
Linear Hypergraphs

For k-graphs F0 and H, an F0-packing of H is a family $\mathscr{F}$ of pairwise edge-disjoint copies of F0 in H. Let νF0(H) denote the maximum size |$\mathscr{F}$| of an F0-packing of H. Already in the case of graphs, computing νF0(H) is NP-hard for most fixed F0 (Dor and Tarsi [6]).In this paper, we consider the case when F0 is a fixed linear k-graph. We establish an algorithm which, for ζ > 0 and a given k-graph H, constructs in time polynomial in |V(H)| an F0-packing of H of size at least νF0(H) − ζ |V(H)|k. Our result extends one of Haxell and Rödl, who established the analogous algorithm for graphs.

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