Embedding spanning subgraphs in uniformly dense and inseparable graphs

Motivated by the definition of the edge elimination polynomial of a graph we define the covered components polynomial counting spanning subgraphs with respect to their number of components, edges and covered components. We prove a recurrence relation, which shows that both graph polynomials are substitution instances of each other. We give some properties of the covered components polynomial and some results concerning relations to other graph polynomials.

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On the Hardness of Constructing Minimal 2-Connected Spanning Subgraphs in Complete Graphs with Sharpened Triangle Inequality

FST TCS 2002: Foundations of Software Technology and Theoretical Computer Science - Lecture Notes in Computer Science ◽

10.1007/3-540-36206-1_7 ◽

2002 ◽

pp. 59-70 ◽

Cited By ~ 8

Author(s):

Hans-Joachim Böckenhauer ◽

Dirk Bongartz ◽

Juraj Hromkovič ◽

Ralf Klasing ◽

Guido Proietti ◽

...

Keyword(s):

Triangle Inequality ◽

Complete Graphs ◽

Spanning Subgraphs

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Long cycles and spanning subgraphs of locally maximal 1‐planar graphs

Journal of Graph Theory ◽

10.1002/jgt.22542 ◽

2020 ◽

Vol 95 (1) ◽

pp. 125-137

Author(s):

I. Fabrici ◽

J. Harant ◽

T. Madaras ◽

S. Mohr ◽

R. Soták ◽

...

Keyword(s):

Planar Graphs ◽

Spanning Subgraphs ◽

Locally Maximal ◽

Long Cycles

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Generating 3-vertex connected spanning subgraphs

Discrete Mathematics ◽

10.1016/j.disc.2007.11.067 ◽

2008 ◽

Vol 308 (24) ◽

pp. 6285-6297 ◽

Cited By ~ 1

Author(s):

Endre Boros ◽

Konrad Borys ◽

Vladimir Gurvich ◽

Gabor Rudolf

Keyword(s):

Spanning Subgraphs

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On spanning subgraphs of a connected bridgeless graph and their application to DT-graphs

Journal of Combinatorial Theory Series B ◽

10.1016/0095-8956(74)90090-2 ◽

1974 ◽

Vol 16 (1) ◽

pp. 17-28 ◽

Cited By ~ 32

Author(s):

Herbert Fleischner

Keyword(s):

Spanning Subgraphs ◽

Bridgeless Graph

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On the Relation of Separability, Bandwidth and Embedding

Graphs and Combinatorics ◽

10.1007/s00373-019-02086-3 ◽

2019 ◽

Vol 35 (6) ◽

pp. 1541-1553

Author(s):

Béla Csaba ◽

Bálint Vásárhelyi

Keyword(s):

Minimum Degree ◽

Bipartite Graphs ◽

Bounded Degree ◽

Spanning Subgraphs ◽

Large Bandwidth

Abstract In this paper we construct a class of bounded degree bipartite graphs with a small separator and large bandwidth, thereby showing that separability and bandwidth are not linearly equivalent. Furthermore, we also prove that graphs from this class are spanning subgraphs of graphs with minimum degree just slightly above n / 2, even though their bandwidth is large.

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