Results 61 to 70 of about 10,864 (212)

A Quasi-Hole Detection Algorithm for Recognizing k-Distance-Hereditary Graphs, with k < 2

Algorithms, 2021
Cicerone and Di Stefano defined and studied the class of k-distance-hereditary graphs, i.e., graphs where the distance in each connected induced subgraph is at most k times the distance in the whole graph. The defined graphs represent a generalization of
Serafino Cicerone
doaj   +1 more source

Complexity of Coloring Graphs without Paths and Cycles

, 2013
Let $P_t$ and $C_\ell$ denote a path on $t$ vertices and a cycle on $\ell$ vertices, respectively. In this paper we study the $k$-coloring problem for $(P_t,C_\ell)$-free graphs.
A. Brandstädt, B. Randerath, B. Randerath, C.T. Hoàng, D. Bruce, D. Král’, D. Leven, G.J. Woeginger, H.J. Broersma, I. Holyer, M. Chudnovsky, M. Grötschel, M. Kamiński, R.E. Tarjan, S. Huang, V.B. Le, Z.. Tuza   +16 more
core   +1 more source

Decomposition of 4k-regular graphs into k 4-regular K5-free and (K5−e)-free subgraphs [PDF]

Discrete Mathematics Letters, 2021
Rachel Johnson, David Mendell, Samantha Norris, Michael J. Plantholt, Shailesh K. Tipnis   +4 more
doaj   +1 more source

Characterizing the forbidden pairs for graphs to be super-edge-connected

AKCE International Journal of Graphs and Combinatorics
Let [Formula: see text] be a set of given connected graphs. A graph G is said to be [Formula: see text]-free if G contains no H as an induced subgraph for any [Formula: see text].
Hazhe Ye, Yingzhi Tian
doaj   +1 more source

On the 12-Representability of Induced Subgraphs of a Grid Graph

Discussiones Mathematicae Graph Theory, 2022
The notion of a 12-representable graph was introduced by Jones, Kitaev, Pyatkin and Remmel in [Representing graphs via pattern avoiding words, Electron. J. Combin. 22 (2015) #P2.53].
Chen Joanna N., Kitaev Sergey
doaj   +1 more source

Advice Complexity of the Online Induced Subgraph Problem [PDF]

, 2015
Several well-studied graph problems aim to select a largest (or smallest) induced subgraph with a given property of the input graph. Examples of such problems include maximum independent set, maximum planar graph, and many others.
Komm, Dennis, Královič, Rastislav, Královič, Richard, Kudahl, Christian   +3 more
core   +2 more sources

On the Caccetta-Häggkvist Conjecture with Forbidden Subgraphs [PDF]

Journal of Graph Theory, 2012
The Caccetta-Haggkvist conjecture made in 1978 asserts that every orgraph on n vertices without oriented cycles of length <= l must contain a vertex of outdegree at most (n-1)/l. It has a rather elaborate set of (conjectured) extremal configurations. In this paper we consider the case l=3 that received quite a significant attention in the literature.
openaire   +3 more sources

Graphs whose Laplacian eigenvalues are almost all 1 or 2

Special Matrices
We explicitly determine all connected graphs whose Laplacian matrices have at most four eigenvalues different from 1 and 2.
Mohammadian Ali, Xu Shanshan
doaj   +1 more source

Minimal Obstructions for Partial Representations of Interval Graphs

, 2015
Interval graphs are intersection graphs of closed intervals. A generalization of recognition called partial representation extension was introduced recently.
C Lekkerkerker, CJ Colbourn, D Skrien, DG Kendall, DR Fulkerson, FS Roberts, G Hajós, K Booth, M Balko, M Patrignani, N Korte, P Klavík, P Klavík, P Klavík, P Klavík, S Benzer, S Chaplick, V Jelínek   +17 more
core   +1 more source

Apex Graphs and Cographs

Theory and Applications of Graphs
A class G of graphs is called hereditary if it is closed under taking induced subgraphs. We denote by G^{apex} the class of graphs G that contain a vertex v such that G − v is in G.
Jagdeep Singh, Vaidy Sivaraman, Thomas Zaslavsky   +2 more
doaj   +1 more source