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Discrete Applied Mathematics, ISSN 0166-218X, 10/2015, Volume 194, pp. 147 - 153
It is well known that a graph is outerplanar if and only if it is K4 -minor free and K2 ,3 -minor free. Campos and Wakabayashi (2013) recently proved that... 
Triangulation | K 4 -minor free graph | Outerplanar graph | K 2 , 3 -minor free graph | Domination number
Journal Article
DISCRETE APPLIED MATHEMATICS, ISSN 0166-218X, 05/2019, Volume 261, pp. 40 - 51
A signed graph (G, Sigma) is a graph G and a subset Sigma of its edges which corresponds to an assignment of signs to the edges: edges in Sigma are negative... 
Edge-coloring | Signed graph | MATHEMATICS, APPLIED | Minor | Homomorphism | Mathematics - Combinatorics
Journal Article
Discrete Mathematics, ISSN 0012-365X, 07/2017, Volume 340, Issue 7, pp. 1633 - 1638
A connected graph G with chromatic number t is double-critical if G∖{x,y} is (t−2)-colorable for each edge xy∈E(G). The complete graphs are the only known... 
Double-critical graphs | Claw-free graphs | Vertex coloring | MATHEMATICS | COMPLETE MINORS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 10/2018, Volume 248, pp. 33 - 45
A graph G is said to be 1-perfectly orientable if it has an orientation D such that for every vertex v∈V(G), the out-neighborhood of v in D is a clique in G.... 
1-perfectly orientable graph | Outerplanar graph | [formula omitted]-minor-free graph | minor-free graph | MINORS | INTERSECTION GRAPHS | MATHEMATICS, APPLIED | SETS | K-4-minor-free graph | SUBTREES
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 05/2018, Volume 88, Issue 1, pp. 154 - 173
We study graphs where each edge that is incident to a vertex of small degree (of degree at most 7 and 9, respectively) belongs to many triangles (at least 4... 
coloration | minors | graph | stress freeness | MATHEMATICS | Computer Science | Discrete Mathematics
Journal Article
Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 11/2016, Volume 121, pp. 284 - 307
A graph H is immersed in a graph G if the vertices of H are mapped to (distinct) vertices of G, and the edges of H are mapped to paths joining the... 
Coloring | Fixed-parameter algorithm | Immersion | MINORS | MATHEMATICS | NUMBER | EVERY PLANAR MAP | HARD | CONJECTURE | Algorithms
Journal Article
Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 01/2018, Volume 128, pp. 114 - 133
We prove that for every graph H, if a graph G has no (odd) H minor, then its vertex set V(G) can be partitioned into three sets X1, X2, X3 such that for each... 
Odd minors | Small components | Vertex partitions | Graph minors | TREE-DECOMPOSITION | MATHEMATICS | HADWIGERS CONJECTURE | WIDTH | Mathematics - Combinatorics
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 2011, Volume 24, Issue 12, pp. 2034 - 2037
The adjacent vertex-distinguishing chromatic index χ a ′ ( G ) of a graph G is the smallest integer k for which G admits a proper edge k -coloring such that... 
Adjacent vertex-distinguishing edge coloring | Maximum degree | [formula omitted]-minor free graph | minor free graph | MATHEMATICS, APPLIED | K-4-minor free graph
Journal Article
Algorithmica, ISSN 0178-4617, 1/2018, Volume 80, Issue 1, pp. 29 - 47
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2016, Volume 30, Issue 2, pp. 955 - 975
Journal Article
Frontiers of Mathematics in China, ISSN 1673-3452, 12/2013, Volume 8, Issue 6, pp. 1351 - 1366
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 04/2013, Volume 482, pp. 20 - 32
The Induced Minor problem is that of testing whether a graph G can be modified into a graph H by a sequence of vertex deletions and edge contractions. If only... 
Induced minor | Contraction | AT-free graphs | COMPUTATIONAL-COMPLEXITY | COMPUTER SCIENCE, THEORY & METHODS
Journal Article
Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 09/2018, Volume 132, pp. 80 - 106
Let Σ be a surface with boundary bd(Σ), L be a collection of k disjoint bd(Σ)-paths in Σ, and P be a non-separating bd(Σ)-path in Σ. We prove that there is a... 
Linkages | Surfaces | Graphs | Minors | MATHEMATICS | DISJOINT PATHS | Algorithms
Journal Article
SIAM JOURNAL ON COMPUTING, ISSN 0097-5397, 2019, Volume 48, Issue 3, pp. 1120 - 1145
We prove that any graph excluding K-r as a minor can be partitioned into clusters of diameter at most Delta while removing at most O(r/Delta) fraction of the... 
EMBEDDING GRAPHS | MATHEMATICS, APPLIED | cops and robber | APPROXIMATION ALGORITHMS | excluded minor | LINEAR-TIME ALGORITHM | COMPUTER SCIENCE, THEORY & METHODS | padded decomposition
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2015, Volume 29, Issue 1, pp. 348 - 375
Paths P-1,..., P-k in a graph G = (V, E) are said to be mutually induced if for any 1 <= i < j <= k, P-i and P-j have neither common vertices nor adjacent... 
Claw-free graphs | Parameterized complexity | Induced disjoint paths | MINORS | parameterized complexity | MATHEMATICS, APPLIED | claw-free graphs | COMPLEXITY | induced disjoint paths
Journal Article
Electronic Notes in Discrete Mathematics, ISSN 1571-0653, 10/2016, Volume 54, pp. 199 - 204
A graph G is said to be 1-perfectly orientable if it has an orientation D such that for every vertex v∈V(G), the out-neighborhood of v in D is a clique in G.... 
K4-minor-free graph | 1-perfectly orientable graph | outerplanar graph | minor-free graph
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 2012, Volume 417, pp. 95 - 107
We improve the running time of the general algorithmic technique known as Baker’s approach (1994) [1] on H -minor-free graphs from O ( n f ( | H | ) ) to O ( f... 
Odd minors | Graph minors | Subexponential algorithms | MINORS | COMPUTER SCIENCE, THEORY & METHODS | Algorithms
Journal Article
by Kim, Y and Lee, SJ and Oum, SI
DISCRETE APPLIED MATHEMATICS, ISSN 0166-218X, 06/2016, Volume 206, pp. 81 - 89
We prove that every simple connected graph with no K5 minor admits a proper 4-coloring such that the neighborhood of each vertex v having more than one... 
Dynamic coloring | MATHEMATICS, APPLIED | Four color theorem | SPERNER CAPACITY | Minor-free graph | Hadwiger's conjecture | SUBGRAPHS | LOCAL CHROMATIC NUMBER | CONJECTURE | Mathematics - Combinatorics
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2016, Volume 30, Issue 2, pp. 832 - 855
A graph is called t-perfect if its stable set polytope is defined by nonnegativity, edge, and odd-cycle inequalities. We show that it can be decided in... 
Claw-free graphs | Induced minors | T-perfect graphs | PATHS PROBLEM | MATHEMATICS, APPLIED | claw-free graphs | t-perfect graphs | SETS | induced minors
Journal Article
Journal of Computer and System Sciences, ISSN 0022-0000, 09/2012, Volume 78, Issue 5, pp. 1606 - 1622
Journal Article
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