Corpus ID: 236493449

The feasability problem for line graphs

@inproceedings{Caro2021TheFP,
  title={The feasability problem for line graphs},
  author={Yair Caro and Josef Lauri and Christina Zarb},
  year={2021}
}
Given F , a family of graphs, and a pair (n,m), n ≥ 1, 0 ≤ m ≤ ( n 2 ) , the pair (n,m) is called feasible (for F ) if there is a graph G ∈ F , with n vertices and m edges. Otherwise (n,m) is called an non-feasible pair. A family of graphs F is called feasible if for every n ≥ 1, every pair (n,m) with 0 ≤ m ≤ ( n 2 ) is feasible, otherwise F is called non-feasible. The minimum/maximum non-feasible pairs problem requires that, for a non-feasible family F , the minimum/maximum value of m such… Expand

Figures from this paper

References

SHOWING 1-10 OF 18 REFERENCES
Absolutely avoidable order-size pairs for induced subgraphs
We call a pair (m, f) of integers, m ≥ 1, 0 ≤ f ≤ ( m 2 ) , absolutely avoidable if there is n0 such that for any pair of integers (n, e) with n > n0 and 0 ≤ e ≤ ( n 2 ) there is a graph on nExpand
Induced subgraphs of given sizes
TLDR
A number of constructions showing that forced pairs are rare are given and infinitely many positive cases are shown. Expand
The sum of the squares of the parts of a partition, and some related questions
Abstract Winkler has proved that, if n and m are positive integers with n ≤ m ≤ n 2 5 and m ≡ n (mod 2), then there exist positive integers {xi} such that Σxi = n and Σx12 = m. Extending work ofExpand
Graph classes characterized both by forbidden subgraphs and degree sequences
TLDR
This work gives a complete characterization of the degree-sequence-forcing sets F when F has cardinality at most two. Expand
Claw-free graphs - A survey
TLDR
This paper summarizes known results on claw-free graphs on n ⩽ 12 vertices and investigates the role of independence, domination, and other invariants in hamiltonicity. Expand
Line Graphs and Forbidden Induced Subgraphs
TLDR
It is shown that a graph with minimum degree at least seven that is not a dumbbell is a line graph if and only if it does not contain three forbidden induced subgraphs including K1, 3 and K5?e. Expand
A Characterization of the degree sequences of 2-trees
TLDR
A characterization of the degree sequences of 2-trees is given and this characterization yields a linear-time algorithm for recognizing and realizing degree sequences in graphs. Expand
Forbidden induced subgraphs for line graphs
  • L. Soltés
  • Computer Science, Mathematics
  • Discret. Math.
  • 1994
Abstract We prove that a connected graph with at least nine vertices is a line graph if and only if it does not contain any of the seven given graphs as an induced subgraph. We also show that theExpand
Characterizations of derived graphs
Abstract The derived graph of a graph G has the edges of G as its vertices, with adjacency determined by the adjacency of the edges in G . A new characterization of derived graphs is given in termsExpand
The History of Degenerate (Bipartite) Extremal Graph Problems
This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe manyExpand
...
1
2
...