MinimumC5-saturated graphs

2009 ◽  
Vol 61 (2) ◽  
pp. 111-126 ◽  
Author(s):  
Ya-Chen Chen
Keyword(s):  
Saturated Graphs

m_Path Cover Saturated Graphs

2003 ◽  
Vol 13 ◽  
pp. 41-44 ◽  
Author(s):  
Aneta Dudek ◽  
Gyula Y. Katona ◽  
A.Pawel Wojda
Keyword(s):  
Saturated Graphs

scholarly journals Few H copies in F ‐saturated graphs

2019 ◽  
Vol 94 (3) ◽  
pp. 320-348 ◽  
Author(s):  
Jürgen Kritschgau ◽  
Abhishek Methuku ◽  
Michael Tait ◽  
Craig Timmons
Keyword(s):  
Saturated Graphs

A Theorem on k-Saturated Graphs

1965 ◽  
Vol 17 ◽  
pp. 720-724 ◽  
Author(s):  
A. Hajnal
Keyword(s):  
Finite Graphs ◽  
Saturated Graphs ◽  
Finite Set ◽  
Multiple Edges

In this paper we consider finite graphs without loops and multiple edges. A graph is considered to be an ordered pair 〈G, *〉 where G is a finite set the elements of which are called the vertices of while * is a subset of [G]2 (where [G]2 is the set of all subsets of two elements of G). The elements of * are called the edges of . If {P, Q} ∊ *, we say that Q is adjacent to P. The degree of a vertex is the number of vertices adjacent to it. Let k be an integer. We say that is the complete k-graph if G has k elements and * = [G]2.

scholarly journals C3 saturated graphs

2005 ◽  
Vol 297 (1-3) ◽  
pp. 152-158 ◽  
Author(s):  
Yehuda Ashkenazi
Keyword(s):  
Saturated Graphs

scholarly journals Minimum degree and the minimum size of K2t-saturated graphs

2007 ◽  
Vol 307 (9-10) ◽  
pp. 1108-1114 ◽  
Author(s):  
Ronald J. Gould ◽  
John R. Schmitt
Keyword(s):  
Minimum Degree ◽  
Minimum Size ◽  
Saturated Graphs

scholarly journals Uniquely (m, k)τ-colourable graphs and k − τ-saturated graphs

1996 ◽  
Vol 162 (1-3) ◽  
pp. 13-22 ◽  
Author(s):  
Gerhard Benadé ◽  
Izak Broere ◽  
Betsie Jonck ◽  
Marietjie Frick
Keyword(s):  
Saturated Graphs

scholarly journals $P_{n}$-Induced-Saturated Graphs Exist for all $n \geqslant 6$

10.37236/9579 ◽  
2020 ◽  
Vol 27 (4) ◽  
Author(s):  
Vojtěch Dvořák
Keyword(s):  
The Other ◽  
Path Graph ◽  
Other Hand ◽  
Saturated Graphs

Let $P_{n}$ be a path graph on $n$ vertices. We say that a graph $G$ is $P_{n}$-induced-saturated if $G$ contains no induced copy of $P_{n}$, but deleting any edge of $G$ as well as adding to $G$ any edge of $G^{c}$ creates such a copy. Martin and Smith (2012) showed that there is no $P_{4}$-induced-saturated graph. On the other hand, there trivially exist $P_{n}$-induced-saturated graphs for $n=2,3$. Axenovich and Csikós (2019) ask for which integers $n \geqslant 5$ do there exist $P_{n}$-induced-saturated graphs. Räty (2019) constructed such a graph for $n=6$, and Cho, Choi and Park (2019) later constructed such graphs for all $n=3k$ for $k \geqslant 2$. We show by a different construction that $P_{n}$-induced-saturated graphs exist for all $n \geqslant 6$, leaving only the case $n=5$ open.

scholarly journals Triangles in Ks-saturated graphs with minimum degree t

2020 ◽  
Vol 07 (01) ◽  
pp. 1-24
Author(s):  
Craig Timmons ◽  
◽  
Benjamin Cole ◽  
Albert Curry ◽  
David Davini
Keyword(s):  
Minimum Degree ◽  
Saturated Graphs
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