Trees and graph packing

2018 ◽  
Author(s):  
Bálint Márk Vásárhelyi
Keyword(s):  
Graph Packing

Induced Graph Packing Problems

2010 ◽  
Vol 26 (2) ◽  
pp. 243-257 ◽  
Author(s):  
Zoltán Király ◽  
Jácint Szabó
Keyword(s):  
Packing Problems ◽  
Graph Packing ◽  
Induced Graph

scholarly journals Extremal Graphs for a Graph Packing Theorem of Sauer and Spencer

2006 ◽  
Vol 16 (03) ◽  
pp. 409 ◽  
Author(s):  
HEMANSHU KAUL ◽  
ALEXANDR KOSTOCHKA
Keyword(s):  
Extremal Graphs ◽  
Graph Packing

scholarly journals On the bipartite graph packing problem

2017 ◽  
Vol 227 ◽  
pp. 149-155 ◽  
Author(s):  
Bálint Vásárhelyi
Keyword(s):  
Bipartite Graph ◽  
Packing Problem ◽  
Graph Packing

A Hypergraph Version of a Graph Packing Theorem by Bollobás and Eldridge

2012 ◽  
Vol 74 (2) ◽  
pp. 222-235
Author(s):  
Alexandr Kostochka ◽  
Christopher Stocker ◽  
Peter Hamburger
Keyword(s):  
Graph Packing

scholarly journals Efficient Graph Packing via Game Colouring

2009 ◽  
Vol 18 (5) ◽  
pp. 765-774 ◽  
Author(s):  
H. A. KIERSTEAD ◽  
A. V. KOSTOCHKA
Keyword(s):  
Game Problem ◽  
The Other ◽  
Graph Packing

The game colouring number gcol(G) of a graphGis the leastksuch that, if two players take turns choosing the vertices of a graph, then either of them can ensure that every vertex has fewer thankneighbours chosen before it, regardless of what choices the other player makes. Clearly gcol(G) ≤ Δ(G)+1. Sauer and Spencer [20] proved that if two graphsG1andG2onnvertices satisfy 2Δ(G1)Δ(G2) <nthen they pack,i.e., there is an embedding ofG1into the complement ofG2. We improve this by showing that if (gcol(G1)−1)Δ(G2)+(gcol(G2)−1)Δ(G1) <nthenG1andG2pack. To our knowledge this is the first application of colouring games to a non-game problem.

scholarly journals Toward Żak’s conjecture on graph packing

2016 ◽  
Vol 7 (2–3) ◽  
pp. 307-340
Author(s):  
Ervin Gyori ◽  
Alexandr Kostochka ◽  
Andrew McConvey ◽  
Derrek Yager
Keyword(s):  
Graph Packing

scholarly journals The Edmonds-Gallai Decomposition for the $k$-Piece Packing Problem

10.37236/1905 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
Marek Janata ◽  
Martin Loebl ◽  
Jácint Szabó
Keyword(s):  
Polynomial Algorithm ◽  
Undirected Graph ◽  
Packing Problem ◽  
Matching Problem ◽  
Graph Packing ◽  
Path Packing ◽  
New Type ◽  
Vertex Sets ◽  
Simple Connected Graph ◽  
Type Decomposition

Generalizing Kaneko's long path packing problem, Hartvigsen, Hell and Szabó consider a new type of undirected graph packing problem, called the $k$-piece packing problem. A $k$-piece is a simple, connected graph with highest degree exactly $k$ so in the case $k=1$ we get the classical matching problem. They give a polynomial algorithm, a Tutte-type characterization and a Berge-type minimax formula for the $k$-piece packing problem. However, they leave open the question of an Edmonds-Gallai type decomposition. This paper fills this gap by describing such a decomposition. We also prove that the vertex sets coverable by $k$-piece packings have a certain matroidal structure.

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