scholarly journals Graph homomorphisms and nodal domains

2006 ◽  
Vol 418 (1) ◽  
pp. 44-52 ◽  
Author(s):  
Amir Daneshgar ◽  
Hossein Hajiabolhassan
Keyword(s):  
Nodal Domains ◽  
Graph Homomorphisms

Graph homomorphisms

2021 ◽  
pp. 262-293
Author(s):  
Pavol Hell ◽  
Jaroslav Nešetřil
Keyword(s):  
Graph Homomorphisms

Graph Operations For Graphic Lattices and Graph Homomorphisms In Topological Cryptosystem

2021 ◽  
Author(s):  
Bing Yao ◽  
Xiaohui Zhang ◽  
Jing Su ◽  
Hui Sun ◽  
Hongyu Wang
Keyword(s):  
Graph Operations ◽  
Graph Homomorphisms

Complexity Dichotomies for Counting Graph Homomorphisms

2016 ◽  
pp. 366-369
Author(s):  
Jin-Yi Cai ◽  
Xi Chen ◽  
Pinyan Lu
Keyword(s):  
Graph Homomorphisms

scholarly journals Another Infinite Sequence of Dense Triangle-Free Graphs

10.37236/1381 ◽  
1998 ◽  
Vol 5 (1) ◽  
Author(s):  
Stephan Brandt ◽  
Tomaž Pisanski
Keyword(s):  
Structural Properties ◽  
Chromatic Number ◽  
Infinite Sequence ◽  
Minimum Degree ◽  
Free Graph ◽  
The Core ◽  
Graph Homomorphisms ◽  
Natural Way

The core is the unique homorphically minimal subgraph of a graph. A triangle-free graph with minimum degree $\delta > n/3$ is called dense. It was observed by many authors that dense triangle-free graphs share strong structural properties and that the natural way to describe the structure of these graphs is in terms of graph homomorphisms. One infinite sequence of cores of dense maximal triangle-free graphs was known. All graphs in this sequence are 3-colourable. Only two additional cores with chromatic number 4 were known. We show that the additional graphs are the initial terms of a second infinite sequence of cores.

scholarly journals Proof of an Intersection Theorem via Graph Homomorphisms

10.37236/1144 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Irit Dinur ◽  
Ehud Friedgut
Keyword(s):  
Product Measure ◽  
Intersection Theorem ◽  
Intersecting Family ◽  
Graph Homomorphisms

Let $0 \leq p \leq 1/2 $ and let $\{0,1\}^n$ be endowed with the product measure $\mu_p$ defined by $\mu_p(x)=p^{|x|}(1-p)^{n-|x|}$, where $|x|=\sum x_i$. Let $I \subseteq \{0,1\}^n$ be an intersecting family, i.e. for every $x, y \in I$ there exists a coordinate $1 \leq i \leq n$ such that $x_i=y_i=1$. Then $\mu_p(I) \leq p.$ Our proof uses measure preserving homomorphisms between graphs.

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