diff --git a/src/Hydra/JsonSchema/SchemaFactory.php b/src/Hydra/JsonSchema/SchemaFactory.php
index 83a1b15e6c..55f443ba2e 100644
--- a/src/Hydra/JsonSchema/SchemaFactory.php
+++ b/src/Hydra/JsonSchema/SchemaFactory.php
@@ -109,7 +109,7 @@ public function buildSchema(string $className, string $format = 'jsonld', string
         // Strictly speaking, it is possible to include `@id` or `@context` in the input,
         // but the generated JSON Schema does not include `"additionalProperties": false` by default,
         // so it is possible to include `@id` or `@context` in the input even if the input schema is a JSON schema.
-        if (Schema::TYPE_INPUT === $type) {
+        if (Schema::TYPE_INPUT === $type && 'jsonapi' !== $format) {
             $format = 'json';
         }
 
diff --git a/src/JsonApi/JsonSchema/SchemaFactory.php b/src/JsonApi/JsonSchema/SchemaFactory.php
index d4b0ab154f..141feb286f 100644
--- a/src/JsonApi/JsonSchema/SchemaFactory.php
+++ b/src/JsonApi/JsonSchema/SchemaFactory.php
@@ -128,6 +128,9 @@ public function buildSchema(string $className, string $format = 'jsonapi', strin
 
         $schema = $this->schemaFactory->buildSchema($className, 'json', $type, $operation, $schema, $jsonApiSerializerContext, $forceCollection);
         $definitionName = $this->definitionNameFactory->create($className, $format, $inputOrOutputClass, $operation, $jsonApiSerializerContext + ['schema_type' => $type]);
+        if (Schema::TYPE_INPUT === $type) {
+            $definitionName .= '.input';
+        }
         $prefix = $this->getSchemaUriPrefix($schema->getVersion());
         $definitions = $schema->getDefinitions();
         $collectionKey = $schema->getItemsDefinitionKey();
@@ -295,7 +298,7 @@ private function buildDefinitionPropertiesSchema(string $key, string $className,
             if ($relation = $this->getRelationship($className, $propertyName, $serializerContext)) {
                 [$isOne, $relatedClasses] = $relation;
                 $refs = [];
-                foreach ($relatedClasses as $relatedClassName => $hasOperations) {
+                foreach (Schema::TYPE_OUTPUT === $type ? $relatedClasses : [] as $relatedClassName => $hasOperations) {
                     if (false === $hasOperations) {
                         continue;
                     }
@@ -358,6 +361,9 @@ private function buildDefinitionPropertiesSchema(string $key, string $className,
                 'type' => 'object',
                 'properties' => $relationships,
             ];
+        }
+
+        if (Schema::TYPE_OUTPUT === $type && \count($relationships) > 0) {
             $included = [
                 'included' => [
                     'description' => 'Related resources requested via the "include" query parameter.',
diff --git a/tests/Functional/OpenApiTest.php b/tests/Functional/OpenApiTest.php
index 7ae7dee890..fc63a7f685 100644
--- a/tests/Functional/OpenApiTest.php
+++ b/tests/Functional/OpenApiTest.php
@@ -138,6 +138,44 @@ public function testOpenApiReferenceInResponsesUsesDollarRef(): void
         $this->assertArrayNotHasKey('ref', $responses['401']);
     }
 
+    public function testNonJsonLdRequestBodiesKeepTheirFormatDefinition(): void
+    {
+        $json = self::createClient()->request('GET', '/docs', [
+            'headers' => ['Accept' => 'application/vnd.openapi+json'],
+        ])->toArray();
+
+        $content = $json['paths']['/dummies']['post']['requestBody']['content'];
+
+        $this->assertSame('#/components/schemas/Dummy', $content['application/xml']['schema']['$ref']);
+        $this->assertSame('#/components/schemas/Dummy', $content['application/ld+json']['schema']['$ref']);
+    }
+
+    public function testJsonApiRequestBodyUsesItsOwnInputDefinition(): void
+    {
+        $json = self::createClient()->request('GET', '/docs', [
+            'headers' => ['Accept' => 'application/vnd.openapi+json'],
+        ])->toArray();
+        $schemas = $json['components']['schemas'];
+
+        $inputName = $this->definitionName($json['paths']['/dummies']['post']['requestBody']['content']['application/vnd.api+json']['schema']['$ref']);
+        $outputName = $this->definitionName($json['paths']['/dummies/{id}']['get']['responses']['200']['content']['application/vnd.api+json']['schema']['$ref']);
+
+        $this->assertSame('Dummy.jsonapi', $outputName);
+        $this->assertNotSame($outputName, $inputName);
+
+        $input = $schemas[$inputName];
+        $this->assertSame(['type'], $input['properties']['data']['required']);
+        $this->assertArrayHasKey('attributes', $input['properties']['data']['properties']);
+        $this->assertArrayNotHasKey('included', $input['properties']);
+
+        $this->assertSame(['type', 'id'], $schemas[$outputName]['properties']['data']['required']);
+    }
+
+    private function definitionName(string $ref): string
+    {
+        return substr($ref, \strlen('#/components/schemas/'));
+    }
+
     public function testDeprecatedPutDoesNotLeakIntoNestedResourceSchema(): void
     {
         $response = self::createClient()->request('GET', '/docs', [