scholarly journals The Topology of Competitively Constructed Graphs

10.37236/3942 ◽  
2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Alan Frieze ◽  
Wesley Pegden
Keyword(s):  
Regular Graph ◽  
Simple Game ◽  
Empty Graph ◽  
Graph Game ◽  
Large Clique

We consider a simple game, the $k$-regular graph game, in which players take turns adding edges to an initially empty graph subject to the constraint that the degrees of vertices cannot exceed $k$. We show a sharp topological threshold for this game: for the case $k=3$ a player can ensure the resulting graph is planar, while for the case $k=4$, a player can force the appearance of arbitrarily large clique minors.

scholarly journals On the Hamiltonicity of the k-Regular Graph Game

2018 ◽  
Vol 34 (6) ◽  
pp. 1131-1145
Author(s):  
Jeremy Meza ◽  
Samuel Simon
Keyword(s):  
Regular Graph ◽  
Graph Game

scholarly journals Connected, Bounded Degree, Triangle Avoidance Games

10.37236/680 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Nishali Mehta ◽  
Ákos Seress
Keyword(s):  
Winning Strategy ◽  
Simple Graph ◽  
Bounded Degree ◽  
Empty Graph ◽  
Graph Game

We consider variants of the triangle-avoidance game first defined by Harary and rediscovered by Hajnal a few years later. A graph game begins with two players and an empty graph on $n$ vertices. The two players take turns choosing edges within $K_{n}$, building up a simple graph. The edges must be chosen according to a set of restrictions $\mathcal{R}$. The winner is the last player to choose an edge that does not violate any of the restrictions in $\mathcal{R}$. For fixed $n$ and $\mathcal{R}$, one of the players has a winning strategy. For a pair of games where $\mathcal{R}$ includes bounded degree, connectedness, and triangle-avoidance, we determine the winner for all values of $n$.

scholarly journals Colouring the Petals of a Graph

10.37236/1699 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
David Cariolaro ◽  
Gianfranco Cariolaro
Keyword(s):  
Regular Graph ◽  
Connected Graph ◽  
Maximum Degree ◽  
Minimum Degree ◽  
Petersen Graph ◽  
Empty Graph ◽  
Single Exception ◽  
Class 1

A petal graph is a connected graph $G$ with maximum degree three, minimum degree two, and such that the set of vertices of degree three induces a $2$–regular graph and the set of vertices of degree two induces an empty graph. We prove here that, with the single exception of the graph obtained from the Petersen graph by deleting one vertex, all petal graphs are Class $1$. This settles a particular case of a conjecture of Hilton and Zhao.

scholarly journals Critical group structure from the parameters of a strongly regular graph

2021 ◽  
Vol 180 ◽  
pp. 105424
Author(s):  
Joshua E. Ducey ◽  
David L. Duncan ◽  
Wesley J. Engelbrecht ◽  
Jawahar V. Madan ◽  
Eric Piato ◽  
...  
Keyword(s):  
Regular Graph ◽  
Group Structure ◽  
Strongly Regular Graph ◽  
Critical Group ◽  
Strongly Regular

scholarly journals Cycle partitions of regular graphs

2020 ◽  
pp. 1-24
Author(s):  
Vytautas Gruslys ◽  
Shoham Letzter
Keyword(s):  
Regular Graph ◽  
Bipartite Graphs ◽  
Disjoint Paths ◽  
Regular Graphs ◽  
Simple Construction ◽  
Vertex Set ◽  
Almost All ◽  
Vertex Disjoint

Abstract Magnant and Martin conjectured that the vertex set of any d-regular graph G on n vertices can be partitioned into $n / (d+1)$ paths (there exists a simple construction showing that this bound would be best possible). We prove this conjecture when $d = \Omega(n)$ , improving a result of Han, who showed that in this range almost all vertices of G can be covered by $n / (d+1) + 1$ vertex-disjoint paths. In fact our proof gives a partition of V(G) into cycles. We also show that, if $d = \Omega(n)$ and G is bipartite, then V(G) can be partitioned into n/(2d) paths (this bound is tight for bipartite graphs).

ON THE REGULAR GRAPH RELATED TO THE G-CONJUGACY CLASSES

2021 ◽  
pp. 1-5
Author(s):  
SH. RAHIMI ◽  
Z. AKHLAGHI
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Conjugacy Class ◽  
Regular Graph ◽  
Simple Graph ◽  
Conjugacy Classes ◽  
A Finite Group

Abstract Given a finite group G with a normal subgroup N, the simple graph $\Gamma _{\textit {G}}( \textit {N} )$ is a graph whose vertices are of the form $|x^G|$ , where $x\in {N\setminus {Z(G)}}$ and $x^G$ is the G-conjugacy class of N containing the element x. Two vertices $|x^G|$ and $|y^G|$ are adjacent if they are not coprime. We prove that, if $\Gamma _G(N)$ is a connected incomplete regular graph, then $N= P \times {A}$ where P is a p-group, for some prime p, $A\leq {Z(G)}$ and $\textbf {Z}(N)\not = N\cap \textbf {Z}(G)$ .

Double Implementation by a Simple Game Form in the Commons Problem

1997 ◽  
Vol 77 (1) ◽  
pp. 205-213 ◽  
Author(s):  
Sungwhee Shin ◽  
Sang-Chul Suh
Keyword(s):  
Simple Game ◽  
Game Form ◽  
The Commons

scholarly journals MovieRemix: Having Fun Playing with Videos

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Nicola Dusi ◽  
Maria Federico ◽  
Marco Furini
Keyword(s):  
Simple Game ◽  
Source Material ◽  
Video Editing ◽  
Technological Aspect ◽  
Server Side ◽  
Challenging Environment ◽  
Streaming Videos ◽  
And Storage ◽  
Client Device ◽  
Different Levels

The process of producing new creative videos by editing, combining, and organizing pre-existing material (e.g., video shots) is a popular phenomenon in the current web scenario. Known asremixor video remix, the produced video may have new and different meanings with respect to the source material. Unfortunately, when managing audiovisual objects, the technological aspect can be a burden for many creative users. Motivated by the large success of the gaming market, we propose a novel game and an architecture to make the remix process a pleasant and stimulating gaming experience. MovieRemix allows people to act like a movie director, but instead of dealing with cast and cameras, the player has to create a remixed video starting from a given screenplay and from video shots retrieved from the provided catalog. MovieRemix is not a simple video editing tool nor is a simple game: it is a challenging environment that stimulates creativity. To temp to play the game, players can access different levels of screenplay (original, outline, derived) and can also challenge other players. Computational and storage issues are kept at the server side, whereas the client device just needs to have the capability of playing streaming videos.

Sign in / Sign up

Export Citation Format

Share Document